# What is the slope of the line perpendicular to  y=-3x-7 ?

May 23, 2018

See a solution process below:

#### Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation 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.

$y = \textcolor{red}{- 3} x - \textcolor{b l u e}{7}$

Therefore, the slope of this line is: $\textcolor{red}{- 3}$

Let's call the slope of a perpendicular line: $\textcolor{b l u e}{{m}_{p}}$

The slope of a line perpendicular to a line with slope $\textcolor{red}{m}$ is the negative inverse, or:

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

Substituting the slope for the line in the problem gives:

$\textcolor{b l u e}{{m}_{p}} = \frac{- 1}{\textcolor{red}{- 3}} = \frac{1}{3}$