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

## 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.

## 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**:

- The slope is given by
**−**.^{a}⁄_{b} - The y-intercept is given by
**−**.^{c}⁄_{b}

## 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.## Step-by-Step:

## 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

## Answer:

We have converted**4x + 2y + 6**(in general form) to**y = −2x − 3**(in slope-intercept form).## You might also like...

linear equationsfinding the y-intercept from a linear equation in general formfinding the equation of a line between two pointsquadratic equations curriculum

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Grammar Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.

## Worksheet

This test is printable and sendable