# In the xy-coordinate plane, the slope of line L is 3 and its y-intercept is 2. what is the equation of the line perpendicular to L that intersects L at its y- intercept?

Feb 13, 2017

$y = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{2}$

#### Explanation:

First, we need to determine the slope of the line perpendicular to L. The slope of L, let's call it ${m}_{L} = 3$. The slope of a perpendicular line, let's call it ${m}_{p}$ is the negative inverse of the slope of line L. Or, ${m}_{p} = - \frac{1}{m} _ L$

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

And, because the y-intercepts are the same we can use the slope-intercept to find the equation for the line in the problem:

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.

Substituting the slope we calculated and the y-intercept from the problem gives:

$y = \textcolor{red}{- \frac{1}{3}} x + \textcolor{b l u e}{2}$