# How do you write the slope intercept form of the line 3x-2y=-16?

May 21, 2017

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

#### Explanation:

Simply make y the subject of the equation:

$- 2 y = - 16 - 3 x$

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

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

May 21, 2017

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

#### Explanation:

Slope intercept form is defined as $y = m x + b$ where $m$ is the slope an $b$ is the $y$-intercept.

In this case we have $3 x - 2 y = - 16$. To write this in slope intercept form we must solve for $y$. Thus,

Subtract $3 x$ to both sides:

$\cancel{3 x - 3 x} - 2 y = - 3 x - 16$

$- 2 y = - 3 x - 16$

Divide $- 2$ to both sides:

$\cancel{- \frac{2}{-} 2} y = \frac{- 3 x - 16}{-} 2$

Simplify:

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

This is now written in slope intercept form where $m$ (the slope) is $\frac{3}{2}$ and our $y$-intercept is $8$