# What is the slope of any line perpendicular to the line passing through (6,26) and (3,41)?

May 3, 2018

$\text{perpendicular slope } = \frac{1}{5}$

#### 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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(6,26)" and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 41\right)$

$\Rightarrow m = \frac{41 - 26}{3 - 6} = \frac{15}{- 3} = - 5$

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