# What is the slope of any line perpendicular to the line passing through (-15,2) and (-10,4)?

Jan 16, 2017

The slope of the perpendicular line is $- \frac{5}{2}$

#### Explanation:

First, we need to determine the slope of the line going through the two points given 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 two points from the problem gives:

$m = \frac{\textcolor{red}{4} - \textcolor{b l u e}{2}}{\textcolor{red}{- 10} - \textcolor{b l u e}{- 15}}$

$m = \frac{\textcolor{red}{4} - \textcolor{b l u e}{2}}{\textcolor{red}{- 10} + \textcolor{b l u e}{15}}$

$m = \frac{2}{5}$

The slope of a perpendicular line is the negative inverse, so we "flip" the slope and take its negative:

${m}_{p} = - \frac{5}{2}$