# How do you find the slope that is perpendicular to the line y = 4x + 5?

Feb 3, 2017

The slope of a perpendicular line will be $- \frac{1}{4}$

#### Explanation:

This equation is in slope-intercept form which is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

Therefore we know the slope of this line is $\textcolor{red}{m = 4}$

A line perpendicular to this line will have a slope (let's call it $\textcolor{b l u e}{{m}_{p}}$) the negative inverse of the slope of the line given in the problem. Or $\textcolor{b l u e}{{m}_{p}} = - \frac{1}{\textcolor{red}{m}}$

Substituting the slope we found above gives:

$\textcolor{b l u e}{{m}_{p}} = - \frac{1}{\textcolor{red}{4}}$