Question

Which of the following lines are perpendicular to y=3x+5? A. 6x+2y-8=0 B. x-3y=-3 C. 12x-24=4y D. 6y=42-2x

Answer 1

The correct answer is D: 6y = 42 - 2x

Explanation:

By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other.

If we transform 6y = 42 - 2x into its slope-intercept form, y = mx + b:

6y = 42 - 2x

6y = -2x + 42

Divide both sides by 6 to isolate y:

`(6y)/(6) = (-2x + 42)/(6)`

y =
`-(1)/(3)x + 7`

Its slope, - 1/3 is the reciprocal of the given question's slope, 3.

Therefore, the correct answer is D, 6y = 42 - 2x