# What is the slope of any line perpendicular to the line passing through (-2,6) and (9,-13)?

Feb 7, 2017

The slope of a perpendicular line is $\frac{11}{19}$

#### Explanation:

First, we need to determine the slope of the line passing through these two points. 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:

$m = \frac{\textcolor{red}{- 13} - \textcolor{b l u e}{6}}{\textcolor{red}{9} - \textcolor{b l u e}{- 2}}$

$m = \frac{\textcolor{red}{- 13} - \textcolor{b l u e}{6}}{\textcolor{red}{9} + \textcolor{b l u e}{2}}$

$m = - \frac{19}{11}$

The slope of a perpendicular line, let's call it ${m}_{p}$ is the negative inverse of the slope of the line it is perpendicular to. Or ${m}_{p} = = \frac{1}{m}$

Therefore the slope of a perpendicular line in this problem is:

${m}_{p} = - - \frac{11}{19}$

${m}_{p} = \frac{11}{19}$