Question

How do you find the slope that is perpendicular to the line `y = 4x + 5`?

Answer 1

The slope of a perpendicular line will be `-1/4`

Explanation:

This equation is in slope-intercept form which 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.

Therefore we know the slope of this line is `color(red)(m = 4)`

A line perpendicular to this line will have a slope (let's call it `color(blue)(m_p)`) the negative inverse of the slope of the line given in the problem. Or `color(blue)(m_p) = -1/color(red)(m)`

Substituting the slope we found above gives:

`color(blue)(m_p) = -1/color(red)(4)`