## General Form of Equation of a Line

Table of Contents

## Definition

General Form of the equation of a straight line is:

*Ax + By + C = 0*

Note:

AorBcan’t be zero at the same time.(if

A = 0thenB ≠ 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:

**6 x − 3y − 9 = 0**

Move all except y to the right:

**−3 y = −6x + 9**

Divide all by (−3):

*y* = 2*x* − 3

And we got ** m = 2** and

*b*=**−3**

Well done!