# What is the slope of any line perpendicular to the line passing through (6,12) and (5,2)?

The slope of any line perpendicular to the line passing through $\left(6 , 12\right)$ and $\left(5 , 2\right)$ is $\left(- \frac{1}{10}\right)$
Slope of a line through $\left(6 , 12\right)$ and $\left(5 , 2\right)$ is
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x} = \frac{12 - 2}{6 - 5} = 10$
If a line has a slope of $m$
$\textcolor{w h i t e}{\text{XXX}}$then every line perpendicular to it has a slope of $- \frac{1}{m}$