# What is the slope of any line perpendicular to the line defined by the equation y = -4x + 1?

Aug 21, 2017

See a solution process below:

#### Explanation:

The equation 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.

$y = \textcolor{red}{- 4} x + \textcolor{b l u e}{1}$

Therefore, the slope of the line represented by the equation in the problem is:

$\textcolor{red}{m = - 4}$

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

The slope of a perpendicular line is:

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

Substituting gives:

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

Aug 21, 2017

The slope is $\frac{1}{4}$

#### Explanation:

The perpendicular slope is expressed as the negative reciprocal of the slope or $- \frac{1}{m}$.

In this scenario, the slope, or $m$, is $- 4$ so the slope of the perpendicular line is $- \frac{1}{- 4}$ which simplifies to $\frac{1}{4}$