## 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).

## Interactive Widget

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