# How do you find the slope that is perpendicular to the line (-3,6) (9,7)?

Jan 26, 2017

See the entire solution process below:

#### Explanation:

First, find the slope of this line using the two points from 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 points from the problem gives:

$m = \frac{\textcolor{red}{7} - \textcolor{b l u e}{6}}{\textcolor{red}{9} - \textcolor{b l u e}{- 3}}$

$m = \frac{\textcolor{red}{7} - \textcolor{b l u e}{6}}{\textcolor{red}{9} + \textcolor{b l u e}{3}}$

$m = \frac{1}{12}$

The slope of a perpendicular line will be the negative inverse, or $- \frac{1}{m}$ of the given line. Taking the negative inverse of the slope we calculated gives:

$- \frac{12}{1} = - 12$

The slope of a perpendicular line will be $- 12$