# How do you find the slope that is perpendicular to the line  y=-2/3x -5?

Jun 25, 2016

$\frac{3}{2}$

#### Explanation:

If $\textcolor{b l u e}{{L}_{1}}$ has a slope of $\textcolor{b l u e}{m}$
and
if $\textcolor{red}{{L}_{2}}$ is perpendicular to $\textcolor{b l u e}{{L}_{1}}$
then
$\textcolor{red}{{L}_{2}}$ has a slope of $\textcolor{red}{- \frac{1}{m}}$

The equation $y = \textcolor{b l u e}{- \frac{2}{3}} x - 5$
is in slope-intercept form with a slope of $\textcolor{b l u e}{m = - \frac{2}{3}}$

Therefore any line perpendicular to it has a slope:
color(white)("XXX")color(red)(-1/(""(color(blue)(-2/3))))=color(red)(3/2)