Question

Consider the line y = 4x + 9. If a second line is perpendicular to this one, what is its slope?

Answer 1

The answer is:

-1/4

Work/explanation:

If two lines are perpendicular to each other, then their slopes are negative inverses of each other.

For example, the slope of the given line (
`\sf{y=4x+9}`) is 4.

The question is, what is the negative inverse of 4?

We need to do two things to 4:

1. Make it negative. (-4)
2. Flip it. -1/4.

Therefore, the slope is -1/4.

Answer 2

Slope of second line = -1/4

Explanation:

The slopes of perpendicular lines are negative reciprocals of each other. We can see this using the following formula:

m2 = -1 / m1, where

• m2 is the slope of the other line (line we're not given),
• and m1 is the slope of the line we're given.

Thus, we plug in 4 for m1 to find m2, the slope of the other line perpendicular to y = 4x + 9:

m2 = -1 / 4

m2 = -1/4

Thus, the slope of the second line perpendicular to y = 4x + 9 is -1/4.