# What is the slope of the line perpendicular to  y=2/3x-6 ?

Aug 19, 2017

Slope of the line perpendicular to $y$ is $- \frac{3}{2}$
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.

$y = \textcolor{red}{\frac{2}{3}} x - \textcolor{b l u e}{6}$

Therefore, the slope of the line represented by the equation in the problem is:

$\textcolor{red}{m = \frac{2}{3}}$

Let's call the slope of a perpendicular line: ${m}_{p}$

The slope of a perpendicular line is:

${m}_{p} = - \frac{1}{m}$

Substituting gives:

${m}_{p} = - \frac{1}{\frac{2}{3}} = - \frac{3}{2}$