# How do you find the slope that is perpendicular to the line 5x + 2y = 6?

##### 1 Answer
Apr 26, 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: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Therefore the slope of $\textcolor{red}{5} x + \textcolor{b l u e}{2} y = \textcolor{g r e e n}{6}$ is:

$m = - \frac{\textcolor{red}{5}}{\textcolor{b l u e}{2}}$

Let the slope of the perpendicular line be: ${m}_{p}$

The formula for the slope of a perpendicular line is:

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

Substituting gives:

${m}_{p} = \frac{- 1}{- \frac{5}{2}} = \frac{2}{5}$