(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
(y-y1)*(x2-x1)=(x-x1)*(y2-y1)
y*x2-y*x1+y1*x1=x*y2-x*y1-x1*y2+x1*y1

x1*y1 si può semplificare; raccogliendo x e y diventa:

y*(x2-x1)-y1*x2=x*(y2-y1)-x1*y2

e quindi:

x*(y2-y1)+y(x1-x2)+(y1*x2-x1*y2)=0

infine:
a = y2-y1
b = x1-x2
c = y1*x2-x1*y2