# Question #af9fd

Mar 16, 2017

$\text{slope "=-2/3" and y-intercept } = 2$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

$\text{Rearrange " 2x+3y=6" into this form}$

subtract 2x from both sides.

$\cancel{2 x} \cancel{- 2 x} + 3 y = - 2 x + 6$

$\Rightarrow 3 y = - 2 x + 6$

divide ALL terms on both sides by 3

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

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

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