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

Jan 7, 2017

Convert to the slope-intercept form and then, using the slope from this form of the equation, take the negative inverse of the slope.

#### Explanation:

First, we need to find the slope of the line given in the problem. To do this we need to put this equation in the 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 color(blue)(b is the y-intercept value.

We can convert the equation from our problem to this form by solving for $y$:

$5 x - 3 y = 2$

$5 x - \textcolor{red}{5 x} - 3 y = - \textcolor{red}{5 x} + 2$

$0 - 3 y = - \textcolor{red}{5 x} + 2$

$- 3 y = - 5 x + 2$

$\frac{- 3 y}{\textcolor{red}{- 3}} = \frac{- 5 x + 2}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} y}{\cancel{\textcolor{red}{- 3}}} = \frac{- 5 x}{\textcolor{red}{- 3}} + \frac{2}{\textcolor{red}{- 3}}$

$y = \frac{5}{3} x - \frac{2}{3}$

The slope of this line is $m = \frac{5}{3}$

For any line with slope $\textcolor{red}{m}$ any line perpendicular to this line will have the negative inverse of the original line or $- \frac{1}{\textcolor{red}{m}}$

Therefore the slope of a line perpendicular to the line in the problem will be:

$- \frac{3}{5}$