# What is the slope and y-intercept of the line 9x+3y=12?

Jun 6, 2016

The slope is $- 3$ and the y-intercept is $4$.

#### Explanation:

It helps if you put your equation into the standard linear form of $y = m x + b$. In this form, $m$ is always the slope, and $b$ is always the y-intercept.

To get it into standard form, you need to isolate $y$. To do this, I can first move the $9 x$ by subtracting it from each side of the equation, giving me:

$3 y = - 9 x + 12$

Then, I would divide each side by 3, to isolate the $y$. The distributive property requires that both $- 9 y$ and $12$ be divided by 3 as well. This gives me:

$y = - 3 x + 4$

Now I have my equation in standard form, and can see that the slope is $- 3$ and the y-intercept is $4$. That can be reflected by graphing the line as well: graph{-3x +4 [-4.834, 5.166, -0.54, 4.46]}