General Form of Equation of a Line


The "General Form" of the equation of a straight line is:

Ax + By + C = 0

A or B can be zero, but not both at the same time.

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

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

y = mx + b

Slope-Intercept Form
or
 

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

y − y1 = m(x − x1)

Point-Slope Form

 

Example: Convert 4x − 2y − 5 = 0 to Slope-Intercept Form

We are heading for

y = mx + b

 

Start with:   4x − 2y − 5 = 0
     
Move all except y to the right:   −2y = −4x + 5
     
Divide all by (−2):   y = 2x − 5/2
     

And we are done! (Note: m = 2 and b = −5/2)

Why Use It?

It has the advantage of working well with vertical lines, which the Slope-Intercept Form and Point-Slope Form do not.