# What is the slope of any line perpendicular to the line passing through (-9,35) and (2,2)?

Aug 5, 2018

$\text{perpendicular slope } = \frac{1}{3}$

#### Explanation:

$\text{calculate the slope m using the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-9,35)" and } \left({x}_{2} , {y}_{2}\right) = \left(2 , 2\right)$

$m = \frac{2 - 35}{2 - \left(- 9\right)} = \frac{- 33}{11} = - 3$

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

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

${m}_{\text{perpendicular}} = - \frac{1}{- 3} = \frac{1}{3}$