How do you find the slope that is perpendicular to the line 3x-5y=-8?

May 25, 2017

See a 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

$\textcolor{red}{3} x - \textcolor{b l u e}{5} y = \textcolor{g r e e n}{- 8}$

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

Substituting and calculating $m$ gives:

$m = \frac{\textcolor{red}{- 3}}{\textcolor{b l u e}{- 5}} = \frac{3}{5}$

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

The formula to find the slope of a perpendicular line is:

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

Substituting the slope we calculated above gives:

${m}_{p} = - \frac{1}{\frac{3}{5}}$

${m}_{p} = - \frac{5}{3}$