# What is the slope of any line perpendicular to the line passing through (-12,14) and (-1,1)?

May 1, 2017

See the solution process below:

#### Explanation:

First, find the slope of the line defined by 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:

$m = \frac{\textcolor{red}{1} - \textcolor{b l u e}{14}}{\textcolor{red}{- 1} - \textcolor{b l u e}{- 12}} = \frac{\textcolor{red}{1} - \textcolor{b l u e}{14}}{\textcolor{red}{- 1} + \textcolor{b l u e}{12}} = - \frac{13}{11}$

Let's call the slope of the perpendicular line ${m}_{p}$

The formula for ${m}_{p}$ is:

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

Substituting the slope we calculated for $m$ and calculating ${m}_{p}$ gives:

${m}_{p} = \frac{- 1}{- \frac{13}{11}} = \frac{11}{13}$

The slope of a perpendicular line is $\frac{11}{13}$