How can I find the general form equation of a line from two points?

Question

Given the input:

double x1,y1,x2,y2;

How can I find the general form equation (double a,b,c where ax + b

Answer 1

If you start from the equation y-y1 = (y2-y1)/(x2-x1) * (x-x1) (which is the equation of the line defined by two points), through some manipulation you can get (y1-y2) * x + (x2-x1) * y + (x1-x2)*y1 + (y2-y1)*x1 = 0, and you can recognize that:

• a = y1-y2,
• b = x2-x1,
• c = (x1-x2)*y1 + (y2-y1)*x1.