# What is the slope of any line perpendicular to the line passing through (-3,-8) and (5,2)?

Jun 18, 2018

$\text{perpendicular slope } = - \frac{4}{5}$

#### Explanation:

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-3,-8)" and } \left({x}_{2} , {y}_{2}\right) = \left(5 , 2\right)$

$m = \frac{2 - \left(- 8\right)}{5 - \left(- 3\right)} = \frac{10}{8} = \frac{5}{4}$

$\text{the perpendicular slope is the "color(blue)"negative reciprocal"" of m}$

${m}_{\text{perpendicular}} = - \frac{1}{m} = - \frac{1}{\frac{5}{4}} = - \frac{4}{5}$