What is the slope of the line perpendicular to  y=-13/2x-5 ?

Mar 10, 2018

Answer:

See a solution process below:

Explanation:

The equation for the line 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.

$y = \textcolor{red}{- \frac{13}{2}} x - \textcolor{b l u e}{5}$

Therefore the slope of this line is: $\textcolor{red}{m = - \frac{13}{2}}$

Let's call the slope of a perpendicular line: $\textcolor{b l u e}{{m}_{p}}$

The slope of a line perpendicular to a line with slope $\textcolor{red}{m}$ is the negative inverse, or:

$\textcolor{b l u e}{{m}_{p}} = - \frac{1}{\textcolor{red}{m}}$

Substituting the slope for the line in the problem gives:

$\textcolor{b l u e}{{m}_{p}} = \frac{- 1}{\textcolor{red}{- \frac{13}{2}}} = \frac{2}{13}$