# How do you write the equation in slope intercept form given 2x + 3y = 12?

Jun 4, 2016

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

#### Explanation:

The slope-intercept form of an equation looks like the following:
$y = m x + b$ , where $m$ is the slope, $x$ is the $x$-value, and $b$ is the indication of the interval the graph is moved up or down.

So, to get the equation from $2 x + 3 y = 12$ into slope intercept form, do the following steps:

1.) Get the $y$ term all by itself.
$3 y = 12 - 2 x$

2.) Get the variable $y$ so that there are no coefficients. This means we need to divide the whole thing by 3 to get y by itself, completely.
$y = 4 - \frac{2}{3} x$

3.) Now rearrange the terms in the right side of the equall sign to get the form of $m x + b$.
$y = - \frac{2}{3} x + 4$

Summary:
We first got the $y$ term by itself (on one side of the equation). Then, we got ride of the coefficient (number before the $y$ variable) by dividing it out. After that, we rearranged the terms $4$ and $- \frac{2}{3} x$ so that it forms $- \frac{2}{3} x + 4$. The final equation is $y = - \frac{2}{3} x + b$. And your equation is in the form $y = m x + b$!