How do you do linear equations with two points?

Answer 1

Suppose you have the points with coordinates (p, q) and (r, s)

then, provided p is different from r,

the slope of the line is (q - s)/(p - r) = m, say.

Then, if (x, y) is any point on the line,

(x - s)/(y - r) = m

That, after simplification, is the linear equation of the line.

This will be a lot simpler when you have numerical values for p, q, r and s rather than work algebraically throughout.

If p is not different from r, then the equation is x = p (or r), a vertical line.