# How do you find the slope and intercept of -3x + 2y = 8?

Jan 7, 2017

To find the slope and y-intercept of this line convert it to the slope-intercept form. See full explanation below.

#### Explanation:

To find the slope and y-intercept of this line convert it to the slope-intercept form.

The slope-intercept form of a linear equation is:

$y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and color(blue)(b is the y-intercept value.

We can solve this equation for $y$ to get it into this format.

$- 3 x + 2 y = 8$

$- 3 x + \textcolor{red}{3 x} + 2 y = \textcolor{red}{3 x} + 8$

$0 + 2 y = 3 x + 8$

$2 y = 3 x + 8$

$\frac{2 y}{\textcolor{red}{2}} = \frac{3 x + 8}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} y}{\cancel{\textcolor{red}{2}}} = \frac{3 x}{\textcolor{red}{2}} + \frac{8}{\textcolor{red}{2}}$

$y = \frac{3}{2} x + 4$

or

$y = \textcolor{red}{\frac{3}{2}} x + \textcolor{b l u e}{4}$

So the slope is $m = \textcolor{red}{\frac{3}{2}}$

And the y-intercept is $b = \textcolor{b l u e}{4}$