# How do you find the slope and intercept to graph 3x+4y=-12?

Mar 28, 2018

$y = - \frac{3}{4} x - 3$

The slope is $- \frac{3}{4}$

The y-intercept is at $\left(0 , - 3\right)$

#### Explanation:

The best way to find the slope and the y-intercept of the given line is to re-write the equation in the slope-intercept form.
That way, you can read the slope and the y-intercept directly from the equation.

The slope-intercept form of an equation is
$y = m x + b$
where $m$ is the slope and $b$ is the y-intercept.

Rewrite the equation in the slope-intercept form

Given 3x+4y=−12    Solve for $y$

1) Subtract $3 x$ from both sides to isolate the $4 y$ term
After you subtract, you will get this:
$4 y = - 3 x - 12$

2) Divide all the terms on both sides by $4$ to isolate $y$
$y = - \frac{3}{4} x - 3$

This equation tells you that the slope is $- \frac{3}{4}$, and that the y-intercept us at $\left(0 , - 3\right)$

Or you can use the Mathway graphing tool to see this line
https://www.mathway.com/PreAlgebra?problem=eT0oMykvKDQpeC0z
(Change the web site's slope of $\frac{3}{4}$ into your wanted slope of $- \frac{3}{4}$ )