# What is the slope of any line perpendicular to the line passing through (29,36) and (57,57)?

Jun 2, 2018

$\text{perpendicular slope } = - \frac{4}{3}$

#### Explanation:

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(29,36)" and } \left({x}_{2} , {y}_{2}\right) = \left(57 , 57\right)$

$m = \frac{57 - 36}{57 - 29} = \frac{21}{28} = \frac{3}{4}$

$\text{the slope of a line perpendicular to m is}$

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

${m}_{\text{perpendicular}} = - \frac{1}{\frac{3}{4}} = - \frac{4}{3}$