# What is the slope of any line perpendicular to the line passing through (-2,8) and (0,4)?

Oct 4, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line passing through 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:

$m = \frac{\textcolor{red}{4} - \textcolor{b l u e}{8}}{\textcolor{red}{0} - \textcolor{b l u e}{- 2}} = \frac{\textcolor{red}{4} - \textcolor{b l u e}{8}}{\textcolor{red}{0} + \textcolor{b l u e}{2}} = - \frac{4}{2} = - 2$

Now, let's call the perpendicular slope ${m}_{p}$. The formula for the perpendicular slope is:

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

Substituting the slope we calculated for $m$ gives:

${m}_{p} = \frac{- 1}{- 2}$

${m}_{p} = \frac{1}{2}$