# How do you find the slope that is perpendicular to the line 4x-3y = -24?

Apr 29, 2017

See the solution process below:

#### Explanation:

This equation is in Standard Form for a linear equation. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Our equation is: $\textcolor{red}{4} x - \textcolor{b l u e}{3} y = \textcolor{g r e e n}{- 24}$

Therefore the slope of the line in the equation is:

$m = \frac{- \textcolor{red}{4}}{\textcolor{b l u e}{- 3}} = \frac{4}{3}$

Let's call the slope of a line perpendicular to the line in the problem:

${m}_{p}$

The formula for a perpendicular line is:

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

Substituting the slope we calculated for $m$ gives:

${m}_{p} = - \frac{1}{\frac{4}{3}} = - \frac{3}{4}$