# What is the slope of any line perpendicular to the line passing through (2,-22) and (18,-4)?

Feb 19, 2017

Any line perpendicular to the line passing through these two points will have a slope of $- \frac{8}{9}$

#### Explanation:

First, we need to find the slope of the line passing through the two points in the problem. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{- 22}}{\textcolor{red}{18} - \textcolor{b l u e}{2}} = \frac{\textcolor{red}{- 4} + \textcolor{b l u e}{22}}{\textcolor{red}{18} - \textcolor{b l u e}{2}} = \frac{18}{16} = \frac{9}{8}$

The slope of the line passing through the two points is $m = \frac{9}{8}$

A line perpendicular to this line will have a slope (let's call it ${m}_{p}$) will have a slope which is the negative inverse of the slope of this line or:

${m}_{p} = - \frac{1}{m}$

Or, ${m}_{p} = - \frac{8}{9}$