## The Lesson

A linear equation is an equation that represents a line. We can convert a linear equation from general form to slope-intercept form.

## Why Convert from General Form to Slope-Intercept Form?

The same line can be written in general form and slope-intercept form. The two forms of linear equation tell us different things about the line.
• In general form, a, b and c do not tell us anything about the line.

• In slope-intercept form, • m tells us the slope of a line • c tells us the y-intercept of a line.

If we are given a line in general form, we can convert it to slope-intercept form to understand more about the line.

## How to Convert a Linear Equation from General to Slope-Intercept Form

Using algebra, we can take the general form of a linear equation and make it look like the slope intercept form.
• Start with the linear equation in general form:

• Subtract ax from both sides. This has the effect of moving the ax to the other side of the equals sign (=) and changing its sign from positive to negative:

• Subtract c from both sides:

• Divide both sides by b:

We can compare this equation with the slope-intercept form of a linear equation:

• The slope is given by ab.
• The y-intercept is given by cb.

## A Real Example of How to Convert a Linear Equation from General to Slope-Intercept Form

Convert the linear equation in general form below to slope-intercept form.

## Question

Find the y-intercept of the line given by the linear equation shown below.

# 1

Subtract 4x from both sides:

4x + 2y + 6 − 4x = 0 − 4x

2y + 6 = −4x

# 2

Subtract 6 from both sides:

2y + 6 − 6 = − 4x − 6

2y = −4x − 6

# 3

Divide both sides by 2:

2y ÷ 2 = (− 4x − 6) ÷ 2

y = −2x − 3

## Answer:

We have converted 4x + 2y + 6 (in general form) to y = −2x − 3 (in slope-intercept form).

## Lesson Slides

The slider below gives a real example of how to convert a linear equation from general form to slope-intercept form. Open the slider in a new tab