# What is the slope of 2x-3y=12?

Apr 16, 2016

$\frac{2}{3}$

#### Explanation:

Turn the standard form of this equation into the slope-intercept form: $y = m x + b$. Remember that $m$ is the slope and $b$ is the y-intercept. We are trying to find for $m$ for this problem.

Bring 2x to the other side of the equal sign by subtracting it from both sides.
$2 x - 2 x - 3 y = 12 - 2 x$

$- 3 y = 12 - 2 x$

Make sure that the coefficient of -3 gets out from $y$ to have $y$ remain isolated. To do so, divide -3 by all of the terms in the equation.
$\frac{- 3 y = 12 - 2 x}{-} 3$

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

Since $m$ is always the coefficient with $x$, we have in this case that $\frac{2}{3}$ is the coefficient with $x$. Therefore, the slope has to be $\frac{2}{3}$.