Writing and Graphing Equations in Point-Slope Form

Concept

Point-Slope Form

A linear equation with slope m through the point (x_1,y_1) is written in the point-slope form if it has the following form.

y-y_1 = m(x-x_1)

In this point-slope equation, (x_1,y_1) represents a specific point on the line, and (x,y) represents any point also on the line. Graphically, this means that the line passes through the point (x_1,y_1).

It is worth mentioning that the point-slope form can only be written for non-vertical lines.

Why

Derivation of the Formula
The point-slope form can be derived by using the Slope Formula. To do so, (x,y) — which represents any point on the line — is substituted for (x_2,y_2) into the formula.

m = y_2-y_1/x_2-x_1
m=y-y_1/x-x_1
m(x-x_1)=y-y_1
y-y_1=m(x-x_1)

Exercises
Edit Lesson