How to write equation of straight line? (3)

Lesson#12
How to write equation of straight line? (3)
CASE 3: If two points of a non-vertical line are given, we will use
Two Point From: y - y1 = y2 - y1/x2 - x1 (x - x1)
We may write this formula in determinant from as
|x y 1|
|x1 y1 1| = 0
|x2 y2 1|
Math.EX4.3 Part 12
Theorem: Equation of a non-vertical straight line passing through two points Q(x1 , y1) and R(x2 , y2)
Proof:
Given: Q(x1 , y1) and R(x2 , y2) are two points on the line.
let P(x , y) be an arbitrary point of the straight line.
Slope of PQ = Slope of QR = Slope of PR
Introduction to Analytical Geometry
Chapter No 4
Exercise No 4.3
Mathematics
part 2