# How do you find the slope that is perpendicular to the line -9x = -6y + 18?

Jul 4, 2017

$\text{slope } = - \frac{2}{3}$

#### Explanation:

$\text{given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

${m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{m}$

$\text{the equation of a line in "color(blue)"slope-intercept form}$ 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.

$\text{to obtain the slope of the given line}$

$\text{rearrange " -9x=-6y+18" into slope-intercept form}$

$\Rightarrow - 6 y = - 9 x - 18$

$\text{divide All terms by - 6}$

$\frac{\cancel{- 6} y}{\cancel{- 6}} = \frac{- 9}{- 6} x - \frac{18}{- 6}$

$\Rightarrow y = \frac{3}{2} x + 3 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$

$\Rightarrow m = \frac{3}{2}$

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{\frac{3}{2}} = - \frac{2}{3}$