# How do you find the slope that is perpendicular to the line x + y = -3?

Jan 25, 2017

See the entire solution process below:

#### Explanation:

First, we need to transform this equation to the slope-intercept form by solving for $y$.

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.

$x + y = - 3$

$x - \textcolor{red}{x} + y = - \textcolor{red}{x} - 3$

$0 + y = - x - 3$

$y = \textcolor{red}{- 1} x - \textcolor{b l u e}{3}$

Therefore the slope of this line is $- 1$.

A line perpendicular to the line in the problem with have a slope which is the negative inverse of the slope of given line or $- \frac{1}{m}$

Substituting the slope we obtained of $- 1$ for $m$ gives:

$- \frac{1}{-} 1 = 1$

The slope of a perpendicular line will have a slope of $1$