[color=#000000]Um ponto P(x, y) pertence à reta r, se e somente se, os vetores [math]\vec{u}[/math]  = (a, b) e [math]\vec{v}[/math] = (x – x[sub]0[/sub], y – y[sub]0[/sub]) forem ortogonais.[/color]

[color=#000000]Da ortogonalidade de [math]\vec{u}[/math]  = (a,b) e [math]\vec{P-P[sub]o[/sub]}  [/math]= ( x - x[sub]0[/sub] , y - y[sub]0 [/sub]) tem-se[/color]:[br][color=#ff0000]a[/color][color=#0000ff](x - x[sub]o)[/sub][/color][color=#0000ff] [/color][color=#000000]+ [/color][color=#ff0000]b[/color][color=#0000ff](y - y[sub]o[/sub]) [/color][color=#000000]= 0[sub] [br][/sub][/color][color=#ff0000]a[/color][color=#0000ff]x[/color][color=#0000ff] [/color][color=#000000]+ [/color][color=#ff0000]b[/color][color=#0000ff]y  [/color][color=#000000]= [/color][color=#ff0000]a[/color][color=#0000ff]x[sub]o[/sub][/color][color=#0000ff] [/color][color=#000000]+ [/color][color=#ff0000]b[/color][color=#0000ff]y[/color][sub][color=#0000ff]o[/color][br][color=#000000][size=100][/size][/color][size=100][color=#000000]Como[/color][color=#0000ff] [/color][color=#ff0000][/color][color=#ff0000]a[/color][color=#0000ff]x[sub]o[/sub][/color][color=#0000ff] [/color][color=#000000]+[/color][color=#000000] [/color][color=#ff0000]b[/color][color=#0000ff]y[sub]o [/sub] [/color][color=#000000]é constante, podemos escrever:[/color][color=#000000][color=#0000ff]  [/color][color=#ff0000]a[/color][color=#0000ff]x[/color][color=#0000ff] [/color][color=#000000]+ [/color][color=#ff0000]b[/color][color=#0000ff]y[/color][color=#0000ff] [/color]= c.[/color][color=#000000][color=#0000ff] [/color][br]Assim, a equação[/color][color=#000000][color=#0000ff] [/color][color=#ff0000]a[/color][color=#0000ff]x[/color][color=#0000ff] [/color][color=#000000]+ [/color][color=#ff0000]b[/color][color=#0000ff]y[/color][color=#0000ff] [/color]= c representa uma reta que passa pelo ponto (0, c/d)  e é ortogonal ao vetor  [math]\vec{u}[/math]  = (a,b).[/color][/size][color=#000000][/color][/sub]