# Find the slope of any line perpendicular to the line passing through (−21,2) and (−32,5)

Find the slope of any line perpendicular to the line passing through (−21,2) and (−32,5)
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Travis Sellers
First we need to find the slope of the line passing through the points: (−21,2) and (−32,5), the slope m between the points:
$\left({x}_{1},{y}_{1}\right)\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}\left({x}_{2},{y}_{2}\right)$ is given by:
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$, so in this case:
$m=\frac{5-2}{-32-\left(-21\right)}$, simplifying we get:
$m=\frac{3}{-32+21}=\frac{3}{-11}=-\frac{3}{11}$
Now the perpendicular lines have slopes that are negative reciprocals, so if ${m}_{1}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}{m}_{2}$ are the slopes of the two perpendicular lines then:
${m}_{2}=-\frac{1}{{m}_{1}}$, therefore in this case:
${m}_{2}=-\frac{1}{-\frac{3}{11}}=\frac{11}{3}$