Question

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

Answer 1

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 = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(-4)x + color(blue)(1)`

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

`color(red)(m = -4)`

Let's call the slope of a perpendicular line: `m_p`

The slope of a perpendicular line is:

`m_p = -1/m`

Substituting gives:

`m_p = (-1)/(-4) = 1/4`

Answer 2

The slope is `1/4`

Explanation:

The perpendicular slope is expressed as the negative reciprocal of the slope or `-1/m`.

In this scenario, the slope, or `m`, is `-4` so the slope of the perpendicular line is `-1/(-4)` which simplifies to `1/4`