# How do you find the slope perpendicular to (-7,2) and (5,-12)?

Mar 2, 2018

${m}_{\text{perpendicular}} = \frac{6}{7}$

#### Explanation:

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

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-7,2)" and } \left({x}_{2} , {y}_{2}\right) = \left(5 , - 12\right)$

$\Rightarrow m = \frac{- 12 - 2}{5 - \left(- 7\right)} = \frac{- 14}{12} = - \frac{7}{6}$

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{- \frac{7}{6}} = \frac{6}{7}$