# What is the slope of any line perpendicular to the line passing through (29,36) and (57,30)?

Jan 31, 2017

First, find the slope of the line passing through these 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 of the points from the problem gives:

$m = \frac{\textcolor{red}{30} - \textcolor{b l u e}{36}}{\textcolor{red}{57} - \textcolor{b l u e}{29}}$

$m = \frac{- 6}{28} = - \frac{6}{28} = - \frac{2 \times 3}{2 \times 14} = - \frac{3}{14}$

A line perpendicular to the line (let's call it ${m}_{p}$) will have the negative inverse slope or ${m}_{p} = - \frac{1}{m}$

Therefore ${m}_{p} = - - \frac{14}{3} = \frac{14}{3}$