# What is the slope of any line perpendicular to the line passing through (1,-7) and (3,-5)?

Jun 14, 2017

See a solution process below:

#### Explanation:

First, we need to find the slope of the line passing through the two points. 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:

$m = \frac{\textcolor{red}{- 5} - \textcolor{b l u e}{- 7}}{\textcolor{red}{3} - \textcolor{b l u e}{1}} = \frac{\textcolor{red}{- 5} + \textcolor{b l u e}{7}}{\textcolor{red}{3} - \textcolor{b l u e}{1}} = \frac{2}{2} = 1$

Let us call the slope of a perpendicular line ${m}_{p}$

The formula for the slope of a perpendicular line is: ${m}_{p} = - \frac{1}{m}$

Substituting the slope we calculated gives us the slope of the perpendicular line as:

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