# What is the slope of any line perpendicular to the line passing through (2,15) and (10,21)?

Aug 30, 2017

See a solution process below:

#### Explanation:

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

$m = \frac{\textcolor{red}{21} - \textcolor{b l u e}{15}}{\textcolor{red}{10} - \textcolor{b l u e}{2}} = \frac{6}{8} = \frac{3}{4}$

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

The slope of a perpendicular can be found using the formula:

${m}_{p} = - \frac{1}{m}$ (This is the negative inverse)

Substituting gives:

${m}_{p} = - \frac{1}{\frac{3}{4}} = - \frac{4}{3}$