# How do you find the slope that is perpendicular to the line x - 5y = -10?

Mar 12, 2018

See a solution process below:

#### Explanation:

This equation is in Standard Linear Form. 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

$\textcolor{red}{1} x - \textcolor{b l u e}{5} y = \textcolor{g r e e n}{- 10}$

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

Substituting gives the slope of the line in the problem as:

$m = - \frac{\textcolor{red}{1}}{\textcolor{b l u e}{- 5}} = \frac{1}{5}$

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

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

$\textcolor{p u r p \le}{{m}_{p}} = - \frac{1}{\textcolor{red}{m}}$

Substituting the slope for the line in the problem gives:

$\textcolor{b l u e}{{m}_{p}} = \frac{- 1}{\textcolor{red}{\frac{1}{5}}} = - 5$