# How do you determine the slope and y-intercept of the graph of 12+3y= -2x?

Oct 5, 2016

slope $= - \frac{2}{3}$
y-intercept = -4

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

The advantage to having the line in this form is that m and b may be extracted 'easily ' from it.

$12 + 3 y = - 2 x \text{ can be written in this form}$

subtract 12 from both sides.

$\cancel{12} \cancel{- 12} + 3 y = - 2 x - 12$

$\Rightarrow 3 y = - 2 x - 12$

divide both sides by 3.

$\frac{\cancel{3} y}{\cancel{3}} = - \frac{2}{3} x - \frac{12}{3}$

$\Rightarrow y = - \frac{2}{3} x - 4 \leftarrow \text{ now in form y=mx+b}$

$\Rightarrow \text{slope" =-2/3" and y-intercept} = - 4$
graph{-2/3x-4 [-10, 10, -5, 5]}