[{"data":1,"prerenderedAt":3208},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fpunkt-steigungs-form":546,"formula-related-de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fpunkt-steigungs-form":3198},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":208,"checks":3101,"conditions":3127,"conditionsHtml":3127,"deprecated":3127,"description":3095,"extension":3128,"figure":3129,"figureCaption":3130,"figureHtml":3165,"formulaId":3166,"latex":3167,"latexHtml":3168,"level":3169,"meta":3170,"navigation":3139,"path":3171,"redirectFrom":3172,"related":3173,"seo":3177,"stem":3178,"subject":582,"summary":3179,"tags":3180,"variables":3185,"__hash__":3197},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fpunkt-steigungs-form.md","Punkt-Steigungs-Form",[550,551,552,553,554],"Punktsteigungsform","Geradengleichung aufstellen","Gerade durch Punkt mit Steigung","Geradengleichung aus zwei Punkten","Funktionsgleichung bestimmen",{"type":556,"value":557,"toc":3094},"minimark",[558,563,807,1060,1151,1155,1279,1518,1659,1850,1881,2053,2187,2191],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571,572,772,773,571,776,806],"p",{},"Eine Gerade ist festgelegt, sobald man ",[568,569,570],"strong",{},"einen Punkt"," ",[573,574,577,628],"span",{"className":575},[576],"katex",[573,578,581],{"className":579},[580],"katex-mathml",[582,583,585],"math",{"xmlns":584},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[586,587,588,623],"semantics",{},[589,590,591,595,600,610,613,620],"mrow",{},[592,593,594],"mi",{},"P",[596,597,599],"mo",{"stretchy":598},"false","(",[601,602,603,606],"msub",{},[592,604,605],{},"x",[607,608,609],"mn",{},"1",[596,611,612],{},"∣",[601,614,615,618],{},[592,616,617],{},"y",[607,619,609],{},[596,621,622],{"stretchy":598},")",[624,625,627],"annotation",{"encoding":626},"application\u002Fx-tex","P(x_1 \\mid y_1)",[573,629,633,720],{"className":630,"ariaHidden":632},[631],"katex-html","true",[573,634,637,642,648,652,708,713,717],{"className":635},[636],"base",[573,638],{"className":639,"style":641},[640],"strut","height:1em;vertical-align:-0.25em;",[573,643,594],{"className":644,"style":647},[645,646],"mord","mathnormal","margin-right:0.1389em;",[573,649,599],{"className":650},[651],"mopen",[573,653,655,658],{"className":654},[645],[573,656,605],{"className":657},[645,646],[573,659,662],{"className":660},[661],"msupsub",[573,663,667,699],{"className":664},[665,666],"vlist-t","vlist-t2",[573,668,671,694],{"className":669},[670],"vlist-r",[573,672,676],{"className":673,"style":675},[674],"vlist","height:0.3011em;",[573,677,679,684],{"style":678},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[573,680],{"className":681,"style":683},[682],"pstrut","height:2.7em;",[573,685,691],{"className":686},[687,688,689,690],"sizing","reset-size6","size3","mtight",[573,692,609],{"className":693},[645,690],[573,695,698],{"className":696},[697],"vlist-s","​",[573,700,702],{"className":701},[670],[573,703,706],{"className":704,"style":705},[674],"height:0.15em;",[573,707],{},[573,709],{"className":710,"style":712},[711],"mspace","margin-right:0.2778em;",[573,714,612],{"className":715},[716],"mrel",[573,718],{"className":719,"style":712},[711],[573,721,723,726,768],{"className":722},[636],[573,724],{"className":725,"style":641},[640],[573,727,729,733],{"className":728},[645],[573,730,617],{"className":731,"style":732},[645,646],"margin-right:0.0359em;",[573,734,736],{"className":735},[661],[573,737,739,760],{"className":738},[665,666],[573,740,742,757],{"className":741},[670],[573,743,745],{"className":744,"style":675},[674],[573,746,748,751],{"style":747},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[573,749],{"className":750,"style":683},[682],[573,752,754],{"className":753},[687,688,689,690],[573,755,609],{"className":756},[645,690],[573,758,698],{"className":759},[697],[573,761,763],{"className":762},[670],[573,764,766],{"className":765,"style":705},[674],[573,767],{},[573,769,622],{"className":770},[771],"mclose"," auf ihr und ihre ",[568,774,775],{},"Steigung",[573,777,779,793],{"className":778},[576],[573,780,782],{"className":781},[580],[582,783,784],{"xmlns":584},[586,785,786,791],{},[589,787,788],{},[592,789,790],{},"m",[624,792,790],{"encoding":626},[573,794,796],{"className":795,"ariaHidden":632},[631],[573,797,799,803],{"className":798},[636],[573,800],{"className":801,"style":802},[640],"height:0.4306em;",[573,804,790],{"className":805},[645,646]," kennt. Die Punkt-Steigungs-Form liefert dann direkt die Geradengleichung, ohne dass man den y-Achsenabschnitt vorher ausrechnen muss.",[564,808,809,810,904,905,935,936,1029,1030,1059],{},"Setzt man ",[573,811,813,836],{"className":812},[576],[573,814,816],{"className":815},[580],[582,817,818],{"xmlns":584},[586,819,820,833],{},[589,821,822,824,827],{},[592,823,605],{},[596,825,826],{},"=",[601,828,829,831],{},[592,830,605],{},[607,832,609],{},[624,834,835],{"encoding":626},"x = x_1",[573,837,839,857],{"className":838,"ariaHidden":632},[631],[573,840,842,845,848,851,854],{"className":841},[636],[573,843],{"className":844,"style":802},[640],[573,846,605],{"className":847},[645,646],[573,849],{"className":850,"style":712},[711],[573,852,826],{"className":853},[716],[573,855],{"className":856,"style":712},[711],[573,858,860,864],{"className":859},[636],[573,861],{"className":862,"style":863},[640],"height:0.5806em;vertical-align:-0.15em;",[573,865,867,870],{"className":866},[645],[573,868,605],{"className":869},[645,646],[573,871,873],{"className":872},[661],[573,874,876,896],{"className":875},[665,666],[573,877,879,893],{"className":878},[670],[573,880,882],{"className":881,"style":675},[674],[573,883,884,887],{"style":678},[573,885],{"className":886,"style":683},[682],[573,888,890],{"className":889},[687,688,689,690],[573,891,609],{"className":892},[645,690],[573,894,698],{"className":895},[697],[573,897,899],{"className":898},[670],[573,900,902],{"className":901,"style":705},[674],[573,903],{}," ein, wird die Klammer ",[573,906,908,922],{"className":907},[576],[573,909,911],{"className":910},[580],[582,912,913],{"xmlns":584},[586,914,915,920],{},[589,916,917],{},[607,918,919],{},"0",[624,921,919],{"encoding":626},[573,923,925],{"className":924,"ariaHidden":632},[631],[573,926,928,932],{"className":927},[636],[573,929],{"className":930,"style":931},[640],"height:0.6444em;",[573,933,919],{"className":934},[645]," und es bleibt ",[573,937,939,961],{"className":938},[576],[573,940,942],{"className":941},[580],[582,943,944],{"xmlns":584},[586,945,946,958],{},[589,947,948,950,952],{},[592,949,617],{},[596,951,826],{},[601,953,954,956],{},[592,955,617],{},[607,957,609],{},[624,959,960],{"encoding":626},"y = y_1",[573,962,964,983],{"className":963,"ariaHidden":632},[631],[573,965,967,971,974,977,980],{"className":966},[636],[573,968],{"className":969,"style":970},[640],"height:0.625em;vertical-align:-0.1944em;",[573,972,617],{"className":973,"style":732},[645,646],[573,975],{"className":976,"style":712},[711],[573,978,826],{"className":979},[716],[573,981],{"className":982,"style":712},[711],[573,984,986,989],{"className":985},[636],[573,987],{"className":988,"style":970},[640],[573,990,992,995],{"className":991},[645],[573,993,617],{"className":994,"style":732},[645,646],[573,996,998],{"className":997},[661],[573,999,1001,1021],{"className":1000},[665,666],[573,1002,1004,1018],{"className":1003},[670],[573,1005,1007],{"className":1006,"style":675},[674],[573,1008,1009,1012],{"style":747},[573,1010],{"className":1011,"style":683},[682],[573,1013,1015],{"className":1014},[687,688,689,690],[573,1016,609],{"className":1017},[645,690],[573,1019,698],{"className":1020},[697],[573,1022,1024],{"className":1023},[670],[573,1025,1027],{"className":1026,"style":705},[674],[573,1028],{},": Die Gerade geht also wirklich durch ",[573,1031,1033,1046],{"className":1032},[576],[573,1034,1036],{"className":1035},[580],[582,1037,1038],{"xmlns":584},[586,1039,1040,1044],{},[589,1041,1042],{},[592,1043,594],{},[624,1045,594],{"encoding":626},[573,1047,1049],{"className":1048,"ariaHidden":632},[631],[573,1050,1052,1056],{"className":1051},[636],[573,1053],{"className":1054,"style":1055},[640],"height:0.6833em;",[573,1057,594],{"className":1058,"style":647},[645,646],".",[564,1061,1062,1063,1066,1067,1059],{},"Typische Anwendung: Gerade durch ",[568,1064,1065],{},"zwei Punkte",". Man berechnet zuerst die Steigung aus beiden Punkten und setzt dann einen der Punkte ein. Durch Ausmultiplizieren erhält man die gewohnte Form ",[573,1068,1070,1096],{"className":1069},[576],[573,1071,1073],{"className":1072},[580],[582,1074,1075],{"xmlns":584},[586,1076,1077,1093],{},[589,1078,1079,1081,1083,1085,1087,1090],{},[592,1080,617],{},[596,1082,826],{},[592,1084,790],{},[592,1086,605],{},[596,1088,1089],{},"+",[592,1091,1092],{},"b",[624,1094,1095],{"encoding":626},"y = mx + b",[573,1097,1099,1117,1141],{"className":1098,"ariaHidden":632},[631],[573,1100,1102,1105,1108,1111,1114],{"className":1101},[636],[573,1103],{"className":1104,"style":970},[640],[573,1106,617],{"className":1107,"style":732},[645,646],[573,1109],{"className":1110,"style":712},[711],[573,1112,826],{"className":1113},[716],[573,1115],{"className":1116,"style":712},[711],[573,1118,1120,1124,1127,1130,1134,1138],{"className":1119},[636],[573,1121],{"className":1122,"style":1123},[640],"height:0.6667em;vertical-align:-0.0833em;",[573,1125,790],{"className":1126},[645,646],[573,1128,605],{"className":1129},[645,646],[573,1131],{"className":1132,"style":1133},[711],"margin-right:0.2222em;",[573,1135,1089],{"className":1136},[1137],"mbin",[573,1139],{"className":1140,"style":1133},[711],[573,1142,1144,1148],{"className":1143},[636],[573,1145],{"className":1146,"style":1147},[640],"height:0.6944em;",[573,1149,1092],{"className":1150},[645,646],[559,1152,1154],{"id":1153},"beispiele","Beispiele",[564,1156,1157,1158,1210,1211,1278],{},"Gerade mit Steigung ",[573,1159,1161,1180],{"className":1160},[576],[573,1162,1164],{"className":1163},[580],[582,1165,1166],{"xmlns":584},[586,1167,1168,1177],{},[589,1169,1170,1172,1174],{},[592,1171,790],{},[596,1173,826],{},[607,1175,1176],{},"3",[624,1178,1179],{"encoding":626},"m = 3",[573,1181,1183,1201],{"className":1182,"ariaHidden":632},[631],[573,1184,1186,1189,1192,1195,1198],{"className":1185},[636],[573,1187],{"className":1188,"style":802},[640],[573,1190,790],{"className":1191},[645,646],[573,1193],{"className":1194,"style":712},[711],[573,1196,826],{"className":1197},[716],[573,1199],{"className":1200,"style":712},[711],[573,1202,1204,1207],{"className":1203},[636],[573,1205],{"className":1206,"style":931},[640],[573,1208,1176],{"className":1209},[645]," durch ",[573,1212,1214,1239],{"className":1213},[576],[573,1215,1217],{"className":1216},[580],[582,1218,1219],{"xmlns":584},[586,1220,1221,1236],{},[589,1222,1223,1225,1227,1230,1232,1234],{},[592,1224,594],{},[596,1226,599],{"stretchy":598},[607,1228,1229],{},"2",[596,1231,612],{},[607,1233,609],{},[596,1235,622],{"stretchy":598},[624,1237,1238],{"encoding":626},"P(2 \\mid 1)",[573,1240,1242,1266],{"className":1241,"ariaHidden":632},[631],[573,1243,1245,1248,1251,1254,1257,1260,1263],{"className":1244},[636],[573,1246],{"className":1247,"style":641},[640],[573,1249,594],{"className":1250,"style":647},[645,646],[573,1252,599],{"className":1253},[651],[573,1255,1229],{"className":1256},[645],[573,1258],{"className":1259,"style":712},[711],[573,1261,612],{"className":1262},[716],[573,1264],{"className":1265,"style":712},[711],[573,1267,1269,1272,1275],{"className":1268},[636],[573,1270],{"className":1271,"style":641},[640],[573,1273,609],{"className":1274},[645],[573,1276,622],{"className":1277},[771],":",[573,1280,1283],{"className":1281},[1282],"katex-display",[573,1284,1286,1346],{"className":1285},[576],[573,1287,1289],{"className":1288},[580],[582,1290,1292],{"xmlns":584,"display":1291},"block",[586,1293,1294,1343],{},[589,1295,1296,1298,1300,1302,1304,1306,1309,1311,1313,1315,1317,1319,1321,1323,1325,1328,1330,1332,1334,1336,1338,1340],{},[592,1297,617],{},[596,1299,826],{},[607,1301,1176],{},[596,1303,599],{"stretchy":598},[592,1305,605],{},[596,1307,1308],{},"−",[607,1310,1229],{},[596,1312,622],{"stretchy":598},[596,1314,1089],{},[607,1316,609],{},[596,1318,826],{},[607,1320,1176],{},[592,1322,605],{},[596,1324,1308],{},[607,1326,1327],{},"6",[596,1329,1089],{},[607,1331,609],{},[596,1333,826],{},[607,1335,1176],{},[592,1337,605],{},[596,1339,1308],{},[607,1341,1342],{},"5",[624,1344,1345],{"encoding":626},"y = 3(x - 2) + 1 = 3x - 6 + 1 = 3x - 5",[573,1347,1349,1367,1391,1412,1430,1452,1470,1488,1509],{"className":1348,"ariaHidden":632},[631],[573,1350,1352,1355,1358,1361,1364],{"className":1351},[636],[573,1353],{"className":1354,"style":970},[640],[573,1356,617],{"className":1357,"style":732},[645,646],[573,1359],{"className":1360,"style":712},[711],[573,1362,826],{"className":1363},[716],[573,1365],{"className":1366,"style":712},[711],[573,1368,1370,1373,1376,1379,1382,1385,1388],{"className":1369},[636],[573,1371],{"className":1372,"style":641},[640],[573,1374,1176],{"className":1375},[645],[573,1377,599],{"className":1378},[651],[573,1380,605],{"className":1381},[645,646],[573,1383],{"className":1384,"style":1133},[711],[573,1386,1308],{"className":1387},[1137],[573,1389],{"className":1390,"style":1133},[711],[573,1392,1394,1397,1400,1403,1406,1409],{"className":1393},[636],[573,1395],{"className":1396,"style":641},[640],[573,1398,1229],{"className":1399},[645],[573,1401,622],{"className":1402},[771],[573,1404],{"className":1405,"style":1133},[711],[573,1407,1089],{"className":1408},[1137],[573,1410],{"className":1411,"style":1133},[711],[573,1413,1415,1418,1421,1424,1427],{"className":1414},[636],[573,1416],{"className":1417,"style":931},[640],[573,1419,609],{"className":1420},[645],[573,1422],{"className":1423,"style":712},[711],[573,1425,826],{"className":1426},[716],[573,1428],{"className":1429,"style":712},[711],[573,1431,1433,1437,1440,1443,1446,1449],{"className":1432},[636],[573,1434],{"className":1435,"style":1436},[640],"height:0.7278em;vertical-align:-0.0833em;",[573,1438,1176],{"className":1439},[645],[573,1441,605],{"className":1442},[645,646],[573,1444],{"className":1445,"style":1133},[711],[573,1447,1308],{"className":1448},[1137],[573,1450],{"className":1451,"style":1133},[711],[573,1453,1455,1458,1461,1464,1467],{"className":1454},[636],[573,1456],{"className":1457,"style":1436},[640],[573,1459,1327],{"className":1460},[645],[573,1462],{"className":1463,"style":1133},[711],[573,1465,1089],{"className":1466},[1137],[573,1468],{"className":1469,"style":1133},[711],[573,1471,1473,1476,1479,1482,1485],{"className":1472},[636],[573,1474],{"className":1475,"style":931},[640],[573,1477,609],{"className":1478},[645],[573,1480],{"className":1481,"style":712},[711],[573,1483,826],{"className":1484},[716],[573,1486],{"className":1487,"style":712},[711],[573,1489,1491,1494,1497,1500,1503,1506],{"className":1490},[636],[573,1492],{"className":1493,"style":1436},[640],[573,1495,1176],{"className":1496},[645],[573,1498,605],{"className":1499},[645,646],[573,1501],{"className":1502,"style":1133},[711],[573,1504,1308],{"className":1505},[1137],[573,1507],{"className":1508,"style":1133},[711],[573,1510,1512,1515],{"className":1511},[636],[573,1513],{"className":1514,"style":931},[640],[573,1516,1342],{"className":1517},[645],[564,1519,1520,1521,1589,1590,1658],{},"Gerade durch ",[573,1522,1524,1550],{"className":1523},[576],[573,1525,1527],{"className":1526},[580],[582,1528,1529],{"xmlns":584},[586,1530,1531,1547],{},[589,1532,1533,1536,1538,1540,1542,1545],{},[592,1534,1535],{},"A",[596,1537,599],{"stretchy":598},[607,1539,609],{},[596,1541,612],{},[607,1543,1544],{},"4",[596,1546,622],{"stretchy":598},[624,1548,1549],{"encoding":626},"A(1 \\mid 4)",[573,1551,1553,1577],{"className":1552,"ariaHidden":632},[631],[573,1554,1556,1559,1562,1565,1568,1571,1574],{"className":1555},[636],[573,1557],{"className":1558,"style":641},[640],[573,1560,1535],{"className":1561},[645,646],[573,1563,599],{"className":1564},[651],[573,1566,609],{"className":1567},[645],[573,1569],{"className":1570,"style":712},[711],[573,1572,612],{"className":1573},[716],[573,1575],{"className":1576,"style":712},[711],[573,1578,1580,1583,1586],{"className":1579},[636],[573,1581],{"className":1582,"style":641},[640],[573,1584,1544],{"className":1585},[645],[573,1587,622],{"className":1588},[771]," und ",[573,1591,1593,1618],{"className":1592},[576],[573,1594,1596],{"className":1595},[580],[582,1597,1598],{"xmlns":584},[586,1599,1600,1615],{},[589,1601,1602,1605,1607,1609,1611,1613],{},[592,1603,1604],{},"B",[596,1606,599],{"stretchy":598},[607,1608,1176],{},[596,1610,612],{},[607,1612,919],{},[596,1614,622],{"stretchy":598},[624,1616,1617],{"encoding":626},"B(3 \\mid 0)",[573,1619,1621,1646],{"className":1620,"ariaHidden":632},[631],[573,1622,1624,1627,1631,1634,1637,1640,1643],{"className":1623},[636],[573,1625],{"className":1626,"style":641},[640],[573,1628,1604],{"className":1629,"style":1630},[645,646],"margin-right:0.0502em;",[573,1632,599],{"className":1633},[651],[573,1635,1176],{"className":1636},[645],[573,1638],{"className":1639,"style":712},[711],[573,1641,612],{"className":1642},[716],[573,1644],{"className":1645,"style":712},[711],[573,1647,1649,1652,1655],{"className":1648},[636],[573,1650],{"className":1651,"style":641},[640],[573,1653,919],{"className":1654},[645],[573,1656,622],{"className":1657},[771],". Zuerst die Steigung:",[573,1660,1662],{"className":1661},[1282],[573,1663,1665,1706],{"className":1664},[576],[573,1666,1668],{"className":1667},[580],[582,1669,1670],{"xmlns":584,"display":1291},[586,1671,1672,1703],{},[589,1673,1674,1676,1678,1697,1699,1701],{},[592,1675,790],{},[596,1677,826],{},[1679,1680,1681,1689],"mfrac",{},[589,1682,1683,1685,1687],{},[607,1684,919],{},[596,1686,1308],{},[607,1688,1544],{},[589,1690,1691,1693,1695],{},[607,1692,1176],{},[596,1694,1308],{},[607,1696,609],{},[596,1698,826],{},[596,1700,1308],{},[607,1702,1229],{},[624,1704,1705],{"encoding":626},"m = \\frac{0 - 4}{3 - 1} = -2",[573,1707,1709,1727,1838],{"className":1708,"ariaHidden":632},[631],[573,1710,1712,1715,1718,1721,1724],{"className":1711},[636],[573,1713],{"className":1714,"style":802},[640],[573,1716,790],{"className":1717},[645,646],[573,1719],{"className":1720,"style":712},[711],[573,1722,826],{"className":1723},[716],[573,1725],{"className":1726,"style":712},[711],[573,1728,1730,1734,1829,1832,1835],{"className":1729},[636],[573,1731],{"className":1732,"style":1733},[640],"height:2.0908em;vertical-align:-0.7693em;",[573,1735,1737,1741,1826],{"className":1736},[645],[573,1738],{"className":1739},[651,1740],"nulldelimiter",[573,1742,1744],{"className":1743},[1679],[573,1745,1747,1817],{"className":1746},[665,666],[573,1748,1750,1814],{"className":1749},[670],[573,1751,1754,1779,1790],{"className":1752,"style":1753},[674],"height:1.3214em;",[573,1755,1757,1761],{"style":1756},"top:-2.314em;",[573,1758],{"className":1759,"style":1760},[682],"height:3em;",[573,1762,1764,1767,1770,1773,1776],{"className":1763},[645],[573,1765,1176],{"className":1766},[645],[573,1768],{"className":1769,"style":1133},[711],[573,1771,1308],{"className":1772},[1137],[573,1774],{"className":1775,"style":1133},[711],[573,1777,609],{"className":1778},[645],[573,1780,1782,1785],{"style":1781},"top:-3.23em;",[573,1783],{"className":1784,"style":1760},[682],[573,1786],{"className":1787,"style":1789},[1788],"frac-line","border-bottom-width:0.04em;",[573,1791,1793,1796],{"style":1792},"top:-3.677em;",[573,1794],{"className":1795,"style":1760},[682],[573,1797,1799,1802,1805,1808,1811],{"className":1798},[645],[573,1800,919],{"className":1801},[645],[573,1803],{"className":1804,"style":1133},[711],[573,1806,1308],{"className":1807},[1137],[573,1809],{"className":1810,"style":1133},[711],[573,1812,1544],{"className":1813},[645],[573,1815,698],{"className":1816},[697],[573,1818,1820],{"className":1819},[670],[573,1821,1824],{"className":1822,"style":1823},[674],"height:0.7693em;",[573,1825],{},[573,1827],{"className":1828},[771,1740],[573,1830],{"className":1831,"style":712},[711],[573,1833,826],{"className":1834},[716],[573,1836],{"className":1837,"style":712},[711],[573,1839,1841,1844,1847],{"className":1840},[636],[573,1842],{"className":1843,"style":1436},[640],[573,1845,1308],{"className":1846},[645],[573,1848,1229],{"className":1849},[645],[564,1851,1852,1853,1278],{},"Dann mit Punkt ",[573,1854,1856,1869],{"className":1855},[576],[573,1857,1859],{"className":1858},[580],[582,1860,1861],{"xmlns":584},[586,1862,1863,1867],{},[589,1864,1865],{},[592,1866,1535],{},[624,1868,1535],{"encoding":626},[573,1870,1872],{"className":1871,"ariaHidden":632},[631],[573,1873,1875,1878],{"className":1874},[636],[573,1876],{"className":1877,"style":1055},[640],[573,1879,1535],{"className":1880},[645,646],[573,1882,1884],{"className":1883},[1282],[573,1885,1887,1933],{"className":1886},[576],[573,1888,1890],{"className":1889},[580],[582,1891,1892],{"xmlns":584,"display":1291},[586,1893,1894,1930],{},[589,1895,1896,1898,1900,1902,1904,1906,1908,1910,1912,1914,1916,1918,1920,1922,1924,1926,1928],{},[592,1897,617],{},[596,1899,826],{},[596,1901,1308],{},[607,1903,1229],{},[596,1905,599],{"stretchy":598},[592,1907,605],{},[596,1909,1308],{},[607,1911,609],{},[596,1913,622],{"stretchy":598},[596,1915,1089],{},[607,1917,1544],{},[596,1919,826],{},[596,1921,1308],{},[607,1923,1229],{},[592,1925,605],{},[596,1927,1089],{},[607,1929,1327],{},[624,1931,1932],{"encoding":626},"y = -2(x - 1) + 4 = -2x + 6",[573,1934,1936,1954,1981,2002,2020,2044],{"className":1935,"ariaHidden":632},[631],[573,1937,1939,1942,1945,1948,1951],{"className":1938},[636],[573,1940],{"className":1941,"style":970},[640],[573,1943,617],{"className":1944,"style":732},[645,646],[573,1946],{"className":1947,"style":712},[711],[573,1949,826],{"className":1950},[716],[573,1952],{"className":1953,"style":712},[711],[573,1955,1957,1960,1963,1966,1969,1972,1975,1978],{"className":1956},[636],[573,1958],{"className":1959,"style":641},[640],[573,1961,1308],{"className":1962},[645],[573,1964,1229],{"className":1965},[645],[573,1967,599],{"className":1968},[651],[573,1970,605],{"className":1971},[645,646],[573,1973],{"className":1974,"style":1133},[711],[573,1976,1308],{"className":1977},[1137],[573,1979],{"className":1980,"style":1133},[711],[573,1982,1984,1987,1990,1993,1996,1999],{"className":1983},[636],[573,1985],{"className":1986,"style":641},[640],[573,1988,609],{"className":1989},[645],[573,1991,622],{"className":1992},[771],[573,1994],{"className":1995,"style":1133},[711],[573,1997,1089],{"className":1998},[1137],[573,2000],{"className":2001,"style":1133},[711],[573,2003,2005,2008,2011,2014,2017],{"className":2004},[636],[573,2006],{"className":2007,"style":931},[640],[573,2009,1544],{"className":2010},[645],[573,2012],{"className":2013,"style":712},[711],[573,2015,826],{"className":2016},[716],[573,2018],{"className":2019,"style":712},[711],[573,2021,2023,2026,2029,2032,2035,2038,2041],{"className":2022},[636],[573,2024],{"className":2025,"style":1436},[640],[573,2027,1308],{"className":2028},[645],[573,2030,1229],{"className":2031},[645],[573,2033,605],{"className":2034},[645,646],[573,2036],{"className":2037,"style":1133},[711],[573,2039,1089],{"className":2040},[1137],[573,2042],{"className":2043,"style":1133},[711],[573,2045,2047,2050],{"className":2046},[636],[573,2048],{"className":2049,"style":931},[640],[573,2051,1327],{"className":2052},[645],[564,2054,2055,2056,2084,2085,2186],{},"Probe mit ",[573,2057,2059,2072],{"className":2058},[576],[573,2060,2062],{"className":2061},[580],[582,2063,2064],{"xmlns":584},[586,2065,2066,2070],{},[589,2067,2068],{},[592,2069,1604],{},[624,2071,1604],{"encoding":626},[573,2073,2075],{"className":2074,"ariaHidden":632},[631],[573,2076,2078,2081],{"className":2077},[636],[573,2079],{"className":2080,"style":1055},[640],[573,2082,1604],{"className":2083,"style":1630},[645,646],": ",[573,2086,2088,2117],{"className":2087},[576],[573,2089,2091],{"className":2090},[580],[582,2092,2093],{"xmlns":584},[586,2094,2095,2114],{},[589,2096,2097,2099,2101,2104,2106,2108,2110,2112],{},[596,2098,1308],{},[607,2100,1229],{},[596,2102,2103],{},"⋅",[607,2105,1176],{},[596,2107,1089],{},[607,2109,1327],{},[596,2111,826],{},[607,2113,919],{},[624,2115,2116],{"encoding":626},"-2 \\cdot 3 + 6 = 0",[573,2118,2120,2141,2159,2177],{"className":2119,"ariaHidden":632},[631],[573,2121,2123,2126,2129,2132,2135,2138],{"className":2122},[636],[573,2124],{"className":2125,"style":1436},[640],[573,2127,1308],{"className":2128},[645],[573,2130,1229],{"className":2131},[645],[573,2133],{"className":2134,"style":1133},[711],[573,2136,2103],{"className":2137},[1137],[573,2139],{"className":2140,"style":1133},[711],[573,2142,2144,2147,2150,2153,2156],{"className":2143},[636],[573,2145],{"className":2146,"style":1436},[640],[573,2148,1176],{"className":2149},[645],[573,2151],{"className":2152,"style":1133},[711],[573,2154,1089],{"className":2155},[1137],[573,2157],{"className":2158,"style":1133},[711],[573,2160,2162,2165,2168,2171,2174],{"className":2161},[636],[573,2163],{"className":2164,"style":931},[640],[573,2166,1327],{"className":2167},[645],[573,2169],{"className":2170,"style":712},[711],[573,2172,826],{"className":2173},[716],[573,2175],{"className":2176,"style":712},[711],[573,2178,2180,2183],{"className":2179},[636],[573,2181],{"className":2182,"style":931},[640],[573,2184,919],{"className":2185},[645],". Stimmt.",[559,2188,2190],{"id":2189},"typische-fehler","Typische Fehler",[2192,2193,2194,2712,2862],"ul",{},[2195,2196,2197,2198,1589,2269,2333,2334,2614,2615,1059],"li",{},"Vorzeichenfehler bei negativen Koordinaten: Für ",[573,2199,2201,2227],{"className":2200},[576],[573,2202,2204],{"className":2203},[580],[582,2205,2206],{"xmlns":584},[586,2207,2208,2224],{},[589,2209,2210,2212,2214,2216,2218,2220,2222],{},[592,2211,594],{},[596,2213,599],{"stretchy":598},[596,2215,1308],{},[607,2217,1229],{},[596,2219,612],{},[607,2221,1176],{},[596,2223,622],{"stretchy":598},[624,2225,2226],{"encoding":626},"P(-2 \\mid 3)",[573,2228,2230,2257],{"className":2229,"ariaHidden":632},[631],[573,2231,2233,2236,2239,2242,2245,2248,2251,2254],{"className":2232},[636],[573,2234],{"className":2235,"style":641},[640],[573,2237,594],{"className":2238,"style":647},[645,646],[573,2240,599],{"className":2241},[651],[573,2243,1308],{"className":2244},[645],[573,2246,1229],{"className":2247},[645],[573,2249],{"className":2250,"style":712},[711],[573,2252,612],{"className":2253},[716],[573,2255],{"className":2256,"style":712},[711],[573,2258,2260,2263,2266],{"className":2259},[636],[573,2261],{"className":2262,"style":641},[640],[573,2264,1176],{"className":2265},[645],[573,2267,622],{"className":2268},[771],[573,2270,2272,2291],{"className":2271},[576],[573,2273,2275],{"className":2274},[580],[582,2276,2277],{"xmlns":584},[586,2278,2279,2288],{},[589,2280,2281,2283,2285],{},[592,2282,790],{},[596,2284,826],{},[607,2286,2287],{},"0,5",[624,2289,2290],{"encoding":626},"m = 0{,}5",[573,2292,2294,2312],{"className":2293,"ariaHidden":632},[631],[573,2295,2297,2300,2303,2306,2309],{"className":2296},[636],[573,2298],{"className":2299,"style":802},[640],[573,2301,790],{"className":2302},[645,646],[573,2304],{"className":2305,"style":712},[711],[573,2307,826],{"className":2308},[716],[573,2310],{"className":2311,"style":712},[711],[573,2313,2315,2319,2322,2330],{"className":2314},[636],[573,2316],{"className":2317,"style":2318},[640],"height:0.8389em;vertical-align:-0.1944em;",[573,2320,919],{"className":2321},[645],[573,2323,2325],{"className":2324},[645],[573,2326,2329],{"className":2327},[2328],"mpunct",",",[573,2331,1342],{"className":2332},[645]," heißt es ",[573,2335,2337,2403],{"className":2336},[576],[573,2338,2340],{"className":2339},[580],[582,2341,2342],{"xmlns":584},[586,2343,2344,2400],{},[589,2345,2346,2348,2350,2352,2354,2356,2358,2360,2362,2364,2366,2368,2370,2372,2374,2376,2378,2380,2382,2384,2386,2388,2390,2392,2394,2396,2398],{},[592,2347,617],{},[596,2349,826],{},[607,2351,2287],{},[596,2353,599],{"stretchy":598},[592,2355,605],{},[596,2357,1308],{},[596,2359,599],{"stretchy":598},[596,2361,1308],{},[607,2363,1229],{},[596,2365,622],{"stretchy":598},[596,2367,622],{"stretchy":598},[596,2369,1089],{},[607,2371,1176],{},[596,2373,826],{},[607,2375,2287],{},[596,2377,599],{"stretchy":598},[592,2379,605],{},[596,2381,1089],{},[607,2383,1229],{},[596,2385,622],{"stretchy":598},[596,2387,1089],{},[607,2389,1176],{},[596,2391,826],{},[607,2393,2287],{},[592,2395,605],{},[596,2397,1089],{},[607,2399,1544],{},[624,2401,2402],{"encoding":626},"y = 0{,}5(x - (-2)) + 3 = 0{,}5(x + 2) + 3 = 0{,}5x + 4",[573,2404,2406,2424,2457,2485,2503,2536,2557,2575,2605],{"className":2405,"ariaHidden":632},[631],[573,2407,2409,2412,2415,2418,2421],{"className":2408},[636],[573,2410],{"className":2411,"style":970},[640],[573,2413,617],{"className":2414,"style":732},[645,646],[573,2416],{"className":2417,"style":712},[711],[573,2419,826],{"className":2420},[716],[573,2422],{"className":2423,"style":712},[711],[573,2425,2427,2430,2433,2439,2442,2445,2448,2451,2454],{"className":2426},[636],[573,2428],{"className":2429,"style":641},[640],[573,2431,919],{"className":2432},[645],[573,2434,2436],{"className":2435},[645],[573,2437,2329],{"className":2438},[2328],[573,2440,1342],{"className":2441},[645],[573,2443,599],{"className":2444},[651],[573,2446,605],{"className":2447},[645,646],[573,2449],{"className":2450,"style":1133},[711],[573,2452,1308],{"className":2453},[1137],[573,2455],{"className":2456,"style":1133},[711],[573,2458,2460,2463,2466,2469,2472,2476,2479,2482],{"className":2459},[636],[573,2461],{"className":2462,"style":641},[640],[573,2464,599],{"className":2465},[651],[573,2467,1308],{"className":2468},[645],[573,2470,1229],{"className":2471},[645],[573,2473,2475],{"className":2474},[771],"))",[573,2477],{"className":2478,"style":1133},[711],[573,2480,1089],{"className":2481},[1137],[573,2483],{"className":2484,"style":1133},[711],[573,2486,2488,2491,2494,2497,2500],{"className":2487},[636],[573,2489],{"className":2490,"style":931},[640],[573,2492,1176],{"className":2493},[645],[573,2495],{"className":2496,"style":712},[711],[573,2498,826],{"className":2499},[716],[573,2501],{"className":2502,"style":712},[711],[573,2504,2506,2509,2512,2518,2521,2524,2527,2530,2533],{"className":2505},[636],[573,2507],{"className":2508,"style":641},[640],[573,2510,919],{"className":2511},[645],[573,2513,2515],{"className":2514},[645],[573,2516,2329],{"className":2517},[2328],[573,2519,1342],{"className":2520},[645],[573,2522,599],{"className":2523},[651],[573,2525,605],{"className":2526},[645,646],[573,2528],{"className":2529,"style":1133},[711],[573,2531,1089],{"className":2532},[1137],[573,2534],{"className":2535,"style":1133},[711],[573,2537,2539,2542,2545,2548,2551,2554],{"className":2538},[636],[573,2540],{"className":2541,"style":641},[640],[573,2543,1229],{"className":2544},[645],[573,2546,622],{"className":2547},[771],[573,2549],{"className":2550,"style":1133},[711],[573,2552,1089],{"className":2553},[1137],[573,2555],{"className":2556,"style":1133},[711],[573,2558,2560,2563,2566,2569,2572],{"className":2559},[636],[573,2561],{"className":2562,"style":931},[640],[573,2564,1176],{"className":2565},[645],[573,2567],{"className":2568,"style":712},[711],[573,2570,826],{"className":2571},[716],[573,2573],{"className":2574,"style":712},[711],[573,2576,2578,2581,2584,2590,2593,2596,2599,2602],{"className":2577},[636],[573,2579],{"className":2580,"style":2318},[640],[573,2582,919],{"className":2583},[645],[573,2585,2587],{"className":2586},[645],[573,2588,2329],{"className":2589},[2328],[573,2591,1342],{"className":2592},[645],[573,2594,605],{"className":2595},[645,646],[573,2597],{"className":2598,"style":1133},[711],[573,2600,1089],{"className":2601},[1137],[573,2603],{"className":2604,"style":1133},[711],[573,2606,2608,2611],{"className":2607},[636],[573,2609],{"className":2610,"style":931},[640],[573,2612,1544],{"className":2613},[645],", nicht ",[573,2616,2618,2646],{"className":2617},[576],[573,2619,2621],{"className":2620},[580],[582,2622,2623],{"xmlns":584},[586,2624,2625,2643],{},[589,2626,2627,2629,2631,2633,2635,2637,2639,2641],{},[607,2628,2287],{},[596,2630,599],{"stretchy":598},[592,2632,605],{},[596,2634,1308],{},[607,2636,1229],{},[596,2638,622],{"stretchy":598},[596,2640,1089],{},[607,2642,1176],{},[624,2644,2645],{"encoding":626},"0{,}5(x - 2) + 3",[573,2647,2649,2682,2703],{"className":2648,"ariaHidden":632},[631],[573,2650,2652,2655,2658,2664,2667,2670,2673,2676,2679],{"className":2651},[636],[573,2653],{"className":2654,"style":641},[640],[573,2656,919],{"className":2657},[645],[573,2659,2661],{"className":2660},[645],[573,2662,2329],{"className":2663},[2328],[573,2665,1342],{"className":2666},[645],[573,2668,599],{"className":2669},[651],[573,2671,605],{"className":2672},[645,646],[573,2674],{"className":2675,"style":1133},[711],[573,2677,1308],{"className":2678},[1137],[573,2680],{"className":2681,"style":1133},[711],[573,2683,2685,2688,2691,2694,2697,2700],{"className":2684},[636],[573,2686],{"className":2687,"style":641},[640],[573,2689,1229],{"className":2690},[645],[573,2692,622],{"className":2693},[771],[573,2695],{"className":2696,"style":1133},[711],[573,2698,1089],{"className":2699},[1137],[573,2701],{"className":2702,"style":1133},[711],[573,2704,2706,2709],{"className":2705},[636],[573,2707],{"className":2708,"style":931},[640],[573,2710,1176],{"className":2711},[645],[2195,2713,2714,1589,2784,2854,2855,2858,2859,1059],{},[573,2715,2717,2735],{"className":2716},[576],[573,2718,2720],{"className":2719},[580],[582,2721,2722],{"xmlns":584},[586,2723,2724,2732],{},[589,2725,2726],{},[601,2727,2728,2730],{},[592,2729,605],{},[607,2731,609],{},[624,2733,2734],{"encoding":626},"x_1",[573,2736,2738],{"className":2737,"ariaHidden":632},[631],[573,2739,2741,2744],{"className":2740},[636],[573,2742],{"className":2743,"style":863},[640],[573,2745,2747,2750],{"className":2746},[645],[573,2748,605],{"className":2749},[645,646],[573,2751,2753],{"className":2752},[661],[573,2754,2756,2776],{"className":2755},[665,666],[573,2757,2759,2773],{"className":2758},[670],[573,2760,2762],{"className":2761,"style":675},[674],[573,2763,2764,2767],{"style":678},[573,2765],{"className":2766,"style":683},[682],[573,2768,2770],{"className":2769},[687,688,689,690],[573,2771,609],{"className":2772},[645,690],[573,2774,698],{"className":2775},[697],[573,2777,2779],{"className":2778},[670],[573,2780,2782],{"className":2781,"style":705},[674],[573,2783],{},[573,2785,2787,2805],{"className":2786},[576],[573,2788,2790],{"className":2789},[580],[582,2791,2792],{"xmlns":584},[586,2793,2794,2802],{},[589,2795,2796],{},[601,2797,2798,2800],{},[592,2799,617],{},[607,2801,609],{},[624,2803,2804],{"encoding":626},"y_1",[573,2806,2808],{"className":2807,"ariaHidden":632},[631],[573,2809,2811,2814],{"className":2810},[636],[573,2812],{"className":2813,"style":970},[640],[573,2815,2817,2820],{"className":2816},[645],[573,2818,617],{"className":2819,"style":732},[645,646],[573,2821,2823],{"className":2822},[661],[573,2824,2826,2846],{"className":2825},[665,666],[573,2827,2829,2843],{"className":2828},[670],[573,2830,2832],{"className":2831,"style":675},[674],[573,2833,2834,2837],{"style":747},[573,2835],{"className":2836,"style":683},[682],[573,2838,2840],{"className":2839},[687,688,689,690],[573,2841,609],{"className":2842},[645,690],[573,2844,698],{"className":2845},[697],[573,2847,2849],{"className":2848},[670],[573,2850,2852],{"className":2851,"style":705},[674],[573,2853],{}," vertauschen: In die Klammer gehört die ",[568,2856,2857],{},"x-Koordinate"," des Punkts, addiert wird die ",[568,2860,2861],{},"y-Koordinate",[2195,2863,2864,2865,2893,2894,2922,2923,2614,3038,1059],{},"Beim Ausmultiplizieren nur das ",[573,2866,2868,2881],{"className":2867},[576],[573,2869,2871],{"className":2870},[580],[582,2872,2873],{"xmlns":584},[586,2874,2875,2879],{},[589,2876,2877],{},[592,2878,605],{},[624,2880,605],{"encoding":626},[573,2882,2884],{"className":2883,"ariaHidden":632},[631],[573,2885,2887,2890],{"className":2886},[636],[573,2888],{"className":2889,"style":802},[640],[573,2891,605],{"className":2892},[645,646]," mit ",[573,2895,2897,2910],{"className":2896},[576],[573,2898,2900],{"className":2899},[580],[582,2901,2902],{"xmlns":584},[586,2903,2904,2908],{},[589,2905,2906],{},[592,2907,790],{},[624,2909,790],{"encoding":626},[573,2911,2913],{"className":2912,"ariaHidden":632},[631],[573,2914,2916,2919],{"className":2915},[636],[573,2917],{"className":2918,"style":802},[640],[573,2920,790],{"className":2921},[645,646]," multiplizieren: ",[573,2924,2926,2960],{"className":2925},[576],[573,2927,2929],{"className":2928},[580],[582,2930,2931],{"xmlns":584},[586,2932,2933,2957],{},[589,2934,2935,2937,2939,2941,2943,2945,2947,2949,2951,2953,2955],{},[607,2936,1176],{},[596,2938,599],{"stretchy":598},[592,2940,605],{},[596,2942,1308],{},[607,2944,1229],{},[596,2946,622],{"stretchy":598},[596,2948,826],{},[607,2950,1176],{},[592,2952,605],{},[596,2954,1308],{},[607,2956,1327],{},[624,2958,2959],{"encoding":626},"3(x - 2) = 3x - 6",[573,2961,2963,2987,3008,3029],{"className":2962,"ariaHidden":632},[631],[573,2964,2966,2969,2972,2975,2978,2981,2984],{"className":2965},[636],[573,2967],{"className":2968,"style":641},[640],[573,2970,1176],{"className":2971},[645],[573,2973,599],{"className":2974},[651],[573,2976,605],{"className":2977},[645,646],[573,2979],{"className":2980,"style":1133},[711],[573,2982,1308],{"className":2983},[1137],[573,2985],{"className":2986,"style":1133},[711],[573,2988,2990,2993,2996,2999,3002,3005],{"className":2989},[636],[573,2991],{"className":2992,"style":641},[640],[573,2994,1229],{"className":2995},[645],[573,2997,622],{"className":2998},[771],[573,3000],{"className":3001,"style":712},[711],[573,3003,826],{"className":3004},[716],[573,3006],{"className":3007,"style":712},[711],[573,3009,3011,3014,3017,3020,3023,3026],{"className":3010},[636],[573,3012],{"className":3013,"style":1436},[640],[573,3015,1176],{"className":3016},[645],[573,3018,605],{"className":3019},[645,646],[573,3021],{"className":3022,"style":1133},[711],[573,3024,1308],{"className":3025},[1137],[573,3027],{"className":3028,"style":1133},[711],[573,3030,3032,3035],{"className":3031},[636],[573,3033],{"className":3034,"style":931},[640],[573,3036,1327],{"className":3037},[645],[573,3039,3041,3061],{"className":3040},[576],[573,3042,3044],{"className":3043},[580],[582,3045,3046],{"xmlns":584},[586,3047,3048,3058],{},[589,3049,3050,3052,3054,3056],{},[607,3051,1176],{},[592,3053,605],{},[596,3055,1308],{},[607,3057,1229],{},[624,3059,3060],{"encoding":626},"3x - 2",[573,3062,3064,3085],{"className":3063,"ariaHidden":632},[631],[573,3065,3067,3070,3073,3076,3079,3082],{"className":3066},[636],[573,3068],{"className":3069,"style":1436},[640],[573,3071,1176],{"className":3072},[645],[573,3074,605],{"className":3075},[645,646],[573,3077],{"className":3078,"style":1133},[711],[573,3080,1308],{"className":3081},[1137],[573,3083],{"className":3084,"style":1133},[711],[573,3086,3088,3091],{"className":3087},[636],[573,3089],{"className":3090,"style":931},[640],[573,3092,1229],{"className":3093},[645],{"title":3095,"searchDepth":3096,"depth":3096,"links":3097},"",2,[3098,3099,3100],{"id":561,"depth":3096,"text":562},{"id":1153,"depth":3096,"text":1154},{"id":2189,"depth":3096,"text":2190},[3102,3105,3108,3113,3116,3121,3123],{"lhs":3103,"rhs":3104},"m*(x1 - x1) + y1","y1",{"lhs":3106,"rhs":3107},"m*(x - x1) + y1","m*x + (y1 - m*x1)",{"lhs":3106,"rhs":3109,"where":3110},"3*x - 5",{"m":3111,"x1":3096,"y1":3112},3,1,{"lhs":3114,"rhs":3115},"(0 - 4)\u002F(3 - 1)","-2",{"lhs":3106,"rhs":3117,"where":3118},"-2*x + 6",{"m":3119,"x1":3112,"y1":3120},-2,4,{"lhs":3122,"rhs":919},"-2*3 + 6",{"lhs":3106,"rhs":3124,"where":3125},"0.5*x + 4",{"m":3126,"x1":3119,"y1":3111},0.5,null,"md",{"caption":3130,"x":3131,"y":3133,"unit":3136,"unitY":3137,"ticks":3138,"axes":3139,"items":3140},"Gerade mit der Steigung m = 3 durch P(2 | 1), also y = 3x − 5",[3132,3120],-1,[3134,3135],-5.6,6,44,24,[3112,3096],true,[3141,3148,3150,3157,3162],{"type":3142,"points":3143,"style":3147},"polygon",[3144,3145,3146],[3096,3112],[3111,3112],[3111,3120],"dashed",{"type":3149,"expr":3109},"function",{"type":3151,"at":3152,"label":3153,"offset":3154},"point",[3096,3112],"P(2 | 1)",[3155,3156],-58,-10,{"type":3158,"at":3159,"text":609,"upright":3139},"label",[3160,3161],2.5,0.45,{"type":3158,"at":3163,"text":790},[3164,3160],3.3,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 220 278.4\" width=\"220\" height=\"278.4\" role=\"img\" aria-label=\"Gerade mit der Steigung m = 3 durch P(2 | 1), also y = 3x − 5\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-point-slope-form-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-point-slope-form-clip\">\u003Crect x=\"0\" y=\"0\" width=\"220\" height=\"278.4\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"144\" x2=\"220\" y2=\"144\" class=\"fig-axis\" marker-end=\"url(#fig-point-slope-form-arrow)\"\u002F>\u003Cline x1=\"44\" y1=\"278.4\" x2=\"44\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-point-slope-form-arrow)\"\u002F>\u003Cline x1=\"0\" y1=\"141\" x2=\"0\" y2=\"147\" class=\"fig-axis\"\u002F>\u003Ctext x=\"3\" y=\"158\" text-anchor=\"start\" class=\"fig-tick\">−1\u003C\u002Ftext>\u003Cline x1=\"88\" y1=\"141\" x2=\"88\" y2=\"147\" class=\"fig-axis\"\u002F>\u003Ctext x=\"91\" y=\"158\" text-anchor=\"start\" class=\"fig-tick\">1\u003C\u002Ftext>\u003Cline x1=\"132\" y1=\"141\" x2=\"132\" y2=\"147\" class=\"fig-axis\"\u002F>\u003Ctext x=\"135\" y=\"158\" text-anchor=\"start\" class=\"fig-tick\">2\u003C\u002Ftext>\u003Cline x1=\"176\" y1=\"141\" x2=\"176\" y2=\"147\" class=\"fig-axis\"\u002F>\u003Ctext x=\"179\" y=\"158\" text-anchor=\"start\" class=\"fig-tick\">3\u003C\u002Ftext>\u003Cline x1=\"41\" y1=\"240\" x2=\"47\" y2=\"240\" class=\"fig-axis\"\u002F>\u003Ctext x=\"38\" y=\"233\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−4\u003C\u002Ftext>\u003Cline x1=\"41\" y1=\"192\" x2=\"47\" y2=\"192\" class=\"fig-axis\"\u002F>\u003Ctext x=\"38\" y=\"185\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">−2\u003C\u002Ftext>\u003Cline x1=\"41\" y1=\"96\" x2=\"47\" y2=\"96\" class=\"fig-axis\"\u002F>\u003Ctext x=\"38\" y=\"89\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">2\u003C\u002Ftext>\u003Cline x1=\"41\" y1=\"48\" x2=\"47\" y2=\"48\" class=\"fig-axis\"\u002F>\u003Ctext x=\"38\" y=\"41\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">4\u003C\u002Ftext>\u003Ctext x=\"214\" y=\"132\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">x\u003C\u002Ftext>\u003Ctext x=\"56\" y=\"8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">y\u003C\u002Ftext>\u003Cpolygon points=\"132,120 176,120 176,48\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 0 336 L 0.92 334.5 L 1.83 333 L 2.75 331.5 L 3.67 330 L 4.58 328.5 L 5.5 327 L 6.42 325.5 L 7.33 324 L 8.25 322.5 L 9.17 321 L 10.08 319.5 L 11 318 L 11.92 316.5 L 12.83 315 L 13.75 313.5 L 14.67 312 L 15.58 310.5 L 16.5 309 L 17.42 307.5 L 18.33 306 L 19.25 304.5 L 20.17 303 L 21.08 301.5 L 22 300 L 22.92 298.5 L 23.83 297 L 24.75 295.5 L 25.67 294 L 26.58 292.5 L 27.5 291 L 28.42 289.5 L 29.33 288 L 30.25 286.5 L 31.17 285 L 32.08 283.5 L 33 282 L 33.92 280.5 L 34.83 279 L 35.75 277.5 L 36.67 276 L 37.58 274.5 L 38.5 273 L 39.42 271.5 L 40.33 270 L 41.25 268.5 L 42.17 267 L 43.08 265.5 L 44 264 L 44.92 262.5 L 45.83 261 L 46.75 259.5 L 47.67 258 L 48.58 256.5 L 49.5 255 L 50.42 253.5 L 51.33 252 L 52.25 250.5 L 53.17 249 L 54.08 247.5 L 55 246 L 55.92 244.5 L 56.83 243 L 57.75 241.5 L 58.67 240 L 59.58 238.5 L 60.5 237 L 61.42 235.5 L 62.33 234 L 63.25 232.5 L 64.17 231 L 65.08 229.5 L 66 228 L 66.92 226.5 L 67.83 225 L 68.75 223.5 L 69.67 222 L 70.58 220.5 L 71.5 219 L 72.42 217.5 L 73.33 216 L 74.25 214.5 L 75.17 213 L 76.08 211.5 L 77 210 L 77.92 208.5 L 78.83 207 L 79.75 205.5 L 80.67 204 L 81.58 202.5 L 82.5 201 L 83.42 199.5 L 84.33 198 L 85.25 196.5 L 86.17 195 L 87.08 193.5 L 88 192 L 88.92 190.5 L 89.83 189 L 90.75 187.5 L 91.67 186 L 92.58 184.5 L 93.5 183 L 94.42 181.5 L 95.33 180 L 96.25 178.5 L 97.17 177 L 98.08 175.5 L 99 174 L 99.92 172.5 L 100.83 171 L 101.75 169.5 L 102.67 168 L 103.58 166.5 L 104.5 165 L 105.42 163.5 L 106.33 162 L 107.25 160.5 L 108.17 159 L 109.08 157.5 L 110 156 L 110.92 154.5 L 111.83 153 L 112.75 151.5 L 113.67 150 L 114.58 148.5 L 115.5 147 L 116.42 145.5 L 117.33 144 L 118.25 142.5 L 119.17 141 L 120.08 139.5 L 121 138 L 121.92 136.5 L 122.83 135 L 123.75 133.5 L 124.67 132 L 125.58 130.5 L 126.5 129 L 127.42 127.5 L 128.33 126 L 129.25 124.5 L 130.17 123 L 131.08 121.5 L 132 120 L 132.92 118.5 L 133.83 117 L 134.75 115.5 L 135.67 114 L 136.58 112.5 L 137.5 111 L 138.42 109.5 L 139.33 108 L 140.25 106.5 L 141.17 105 L 142.08 103.5 L 143 102 L 143.92 100.5 L 144.83 99 L 145.75 97.5 L 146.67 96 L 147.58 94.5 L 148.5 93 L 149.42 91.5 L 150.33 90 L 151.25 88.5 L 152.17 87 L 153.08 85.5 L 154 84 L 154.92 82.5 L 155.83 81 L 156.75 79.5 L 157.67 78 L 158.58 76.5 L 159.5 75 L 160.42 73.5 L 161.33 72 L 162.25 70.5 L 163.17 69 L 164.08 67.5 L 165 66 L 165.92 64.5 L 166.83 63 L 167.75 61.5 L 168.67 60 L 169.58 58.5 L 170.5 57 L 171.42 55.5 L 172.33 54 L 173.25 52.5 L 174.17 51 L 175.08 49.5 L 176 48 L 176.92 46.5 L 177.83 45 L 178.75 43.5 L 179.67 42 L 180.58 40.5 L 181.5 39 L 182.42 37.5 L 183.33 36 L 184.25 34.5 L 185.17 33 L 186.08 31.5 L 187 30 L 187.92 28.5 L 188.83 27 L 189.75 25.5 L 190.67 24 L 191.58 22.5 L 192.5 21 L 193.42 19.5 L 194.33 18 L 195.25 16.5 L 196.17 15 L 197.08 13.5 L 198 12 L 198.92 10.5 L 199.83 9 L 200.75 7.5 L 201.67 6 L 202.58 4.5 L 203.5 3 L 204.42 1.5 L 205.33 0 L 206.25 -1.5 L 207.17 -3 L 208.08 -4.5 L 209 -6 L 209.92 -7.5 L 210.83 -9 L 211.75 -10.5 L 212.67 -12 L 213.58 -13.5 L 214.5 -15 L 215.42 -16.5 L 216.33 -18 L 217.25 -19.5 L 218.17 -21 L 219.08 -22.5 L 220 -24\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-point-slope-form-clip)\"\u002F>\u003Ccircle cx=\"132\" cy=\"120\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"74\" y=\"110\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">P(2 | 1)\u003C\u002Ftext>\u003Ctext x=\"154\" y=\"133.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">1\u003C\u002Ftext>\u003Ctext x=\"189.2\" y=\"84\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">m\u003C\u002Ftext>\u003C\u002Fsvg>","point-slope-form","y = m(x - x_1) + y_1","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>m\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y = m(x - x_1) + y_1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fpunkt-steigungs-form",[],[3174,3175,3176],"linear-function","slope-two-points","perpendicular-lines",{"title":548,"description":3095},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fpunkt-steigungs-form","Stellt die Gleichung einer Geraden auf, wenn ihre Steigung m und ein Punkt P(x₁ | y₁) auf ihr bekannt sind.",[3181,3182,3183,3184],"gerade","steigung","geradengleichung","funktionsgleichung",[3186,3189,3193],{"symbol":790,"meaning":3187,"symbolHtml":3188},"Steigung der Geraden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">m\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3190,"meaning":3191,"symbolHtml":3192},"x_1, y_1","Koordinaten eines bekannten Punkts P(x₁ | y₁) auf der Geraden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_1, y_1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3194,"meaning":3195,"symbolHtml":3196},"x, y","Koordinaten eines beliebigen Punkts auf der Geraden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x, y\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","q4IA-RmLSXBRdV5zNGex6eurXPRaxXXBpsclYhmrZ1c",[3199,3202,3205],{"stem":3200,"title":3201,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Flineare-funktion","Lineare Funktion",{"stem":3203,"title":3204,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Forthogonale-geraden","Orthogonale Geraden",{"stem":3206,"title":3207,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fsteigung-aus-zwei-punkten","Steigung aus zwei Punkten",1793824274941]