# What is the slope of any line perpendicular to the line passing through (13,17) and (-1,-2)?

Mar 5, 2018

See a solution process below:

#### Explanation:

First, we can 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:

$m = \frac{\textcolor{red}{- 2} - \textcolor{b l u e}{17}}{\textcolor{red}{- 1} - \textcolor{b l u e}{13}} = \frac{- 19}{-} 14 = \frac{19}{14}$

One of the characteristics of perpendicular lines is their slopes are the negative inverse of each other. In other words, if the slope of one line is: $m$

Then the slope of the perpendicular line, let's call it ${m}_{p}$, is

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

We can calculate the slope of a perpendicular line as:

${m}_{p} = - \frac{1}{\frac{19}{14}} = - \frac{14}{19}$

Any line perpendicular to the line in the problem will have a slope of:

$m = - \frac{14}{19}$