General Form of Equation of a Line

Definition

General Form of the equation of a straight line is:

Ax + By + C = 0

Note:

A or B can’t be zero at the same time.

(if A = 0 then B ≠ 0, vice versa)

The General Form is not always the most useful form, and you may prefer to use:

Slope-Intercept Form Of The Equation Of a Line

Slope-Intercept Form of the equation of a straight line is:

y = mx + b

Point-Slope Form of the equation of a line

Point-Slope Form of the equation of a straight line is:

y − y1 = m(x − x1)

Example

Convert 6x − 3y − 9 = 0 to Slope-Intercept Form

We are heading for:

y = mx + b

Start with:

6x − 3y − 9 = 0

Move all except y to the right:

−3y = −6x + 9

Divide all by (−3):   

y = 2x − 3

And we got m = 2 and b = −3

Well done!

Learn More

Zero Product Property

Partial Sum

Directly and Inversely Proportional

Finding an Angle in a Right Angled Triangle

Algebra Index

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