# What is the slope of any line perpendicular to the line passing through (-5,1) and (-14,-4)?

Aug 21, 2017

See a solution process below:

#### Explanation:

First, we need to find the slope of the line containing 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:

$m = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{1}}{\textcolor{red}{- 14} - \textcolor{b l u e}{- 5}} = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{1}}{\textcolor{red}{- 14} + \textcolor{b l u e}{5}} = \frac{- 5}{-} 9 = \frac{5}{9}$

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

The slope of a perpendicular line is:

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

Substituting gives:

${m}_{p} = - \frac{1}{\frac{5}{9}} = - \frac{9}{5}$