Question

Which line is perpendicular to the line y = -3x + 2?

A) 3x + y = 4
B) x + 3y = 24
C) 3x - y = 5
D) x - 3y = 3

Answer 1

The lines x + 3y = 24 and x - 3y = 3 are perpendicular to y = -3x + 2.

Step-by-step explanation:

To determine which line is perpendicular to y = -3x + 2, we need to find the line with a slope that is the negative reciprocal of -3. The negative reciprocal of -3 is 1/3, so any line with a slope of 1/3 will be perpendicular to y = -3x + 2.

Let's check the slopes of the given options:

1. A) 3x + y = 4: The slope is -3/1, which is not perpendicular.
2. B) x + 3y = 24: Rearranging the equation in slope-intercept form gives y = -1/3x + 8. The slope is -1/3, which is perpendicular.
3. C) 3x - y = 5: Rearranging the equation in slope-intercept form gives y = 3x - 5. The slope is 3, which is not perpendicular.
4. D) x - 3y = 3: Rearranging the equation in slope-intercept form gives y = 1/3x - 1. The slope is 1/3, which is perpendicular.

Therefore, the lines B) x + 3y = 24 and D) x - 3y = 3 are perpendicular to y = -3x + 2.