# What is the slope of a line parallel and perpendicular to the line going through: (-7, -3) and (6, 8)?

Apr 10, 2017

See the entire solution process below:

#### Explanation:

First, find the slope of the line going through the 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:

$m = \frac{\textcolor{red}{8} - \textcolor{b l u e}{- 3}}{\textcolor{red}{6} - \textcolor{b l u e}{- 7}} = \frac{\textcolor{red}{8} + \textcolor{b l u e}{3}}{\textcolor{red}{6} + \textcolor{b l u e}{7}} = \frac{11}{13}$

A line parallel to this line will have the same slope as this line. Therefore, the slope of a parallel line will be: $m = \frac{11}{13}$

Let's call the slope of a perpendicular line ${m}_{p}$. The slope of a perpendicular line is:

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

Therefore, the slope of a perpendicular line is: ${m}_{p} = - \frac{13}{11}$