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Concept

Point-Slope Form

A linear equation with slope m through the point (x1,y1) is written in the point-slope form if it has the following form.

y−y1=m(x−x1)

In this equation, (x1,y1) 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 (x1,y1).

graph of a line in point-slope form

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

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Why

Derivation of the Formula

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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 (x2,y2) into the formula.
SubstituteII

x2=x, y2=y

MultEqn

LHS⋅(x−x1)=RHS⋅(x−x1)

m(x−x1)=y−y1
RearrangeEqn

Rearrange equation

y−y1=m(x−x1)
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