# How do you find the slope that is perpendicular to the line 3x+2y=-5?

Dec 26, 2016

$\frac{2}{3}$

#### Explanation:

To find the slope of a perpendicular line we must first find the slope of line given in the problem. To do this we must transform this equation into the slope-intercept format.

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.

Solving the equation in the problem for $y$ produces:

$3 x - \textcolor{g r e e n}{3 x} + 2 y = - \textcolor{g r e e n}{3 x} - 5$

$0 + 2 y = - 3 x - 5$

$2 y = - 3 x - 5$

$\frac{2 y}{\textcolor{g r e e n}{2}} = \frac{- 3 x - 5}{\textcolor{g r e e n}{2}}$

$\frac{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{2}}} y}{\cancel{\textcolor{g r e e n}{2}}} = - \frac{3}{2} x - \frac{5}{2}$

$y = \textcolor{red}{- \frac{3}{2}} x - \textcolor{b l u e}{\frac{5}{2}}$

Therefore the slope of this line is $\textcolor{red}{m} = - \frac{3}{2}$

The slope of a perpendicular line is the negative inverse of the slope of the line we are given, or $\textcolor{red}{- \frac{1}{m}}$

So, for our problem the slope of a perpendicular line is $\textcolor{red}{- - \frac{2}{3} = \frac{2}{3}}$