# How do you write the equation in slope intercept form given 3x - 2y = -6?

May 10, 2018

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

#### Explanation:

The slope intercept form of a line is given as:

$y = m x + b$

Where:

$\boldsymbol{m}$ is the gradient and $\boldsymbol{b}$ is the y axis intercept.

Our task is to rearrange our function so it is in the same form.

$3 x - 2 y = - 6$

Subtract $3 x$ from both sides:

$3 x - 3 x - 2 y = - 6 - 3 x$

$- 2 y = - 6 - 3 x$

Divide both sides by $- 2$

$\frac{- 2 y}{- 2} = \frac{- 6}{- 2} \setminus \setminus \frac{- 3 x}{- 2}$

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

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