# What is the slope of any line perpendicular to the line passing through (-6,1) and (-2,5)?

Apr 27, 2017

First we need to determine the slope of the line passing through the two points in the problem. The formula for calculating the slope is:

$m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ and $\left(\textcolor{red}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right)$ are two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{5} - \textcolor{b l u e}{1}}{\textcolor{red}{- 2} - \textcolor{b l u e}{- 6}} = \frac{\textcolor{red}{5} - \textcolor{b l u e}{1}}{\textcolor{red}{- 2} + \textcolor{b l u e}{6}} = \frac{4}{4} = 1$

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

The rule for calculating the slope of a perpendicular line is:

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

Substituting the slope we calculated gives:

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