Algebra practice question

Answer: D. y = −(3/2)x + 7

Perpendicular slopes are negative reciprocals. The negative reciprocal of 2/3 is −3/2, so choice D works. Choice A (same slope) is parallel; choice C only negates the slope without taking the reciprocal.

Why the other answers are wrong

A. y = (2/3)x − 4

Slope 2/3 matches line k exactly, so this line is parallel, not perpendicular. You need the negative reciprocal, −3/2.

B. y = (3/2)x + 5

You flipped 2/3 to 3/2 but never made it negative. Perpendicular slopes must multiply to −1, so the slope you want is −3/2.

C. y = −(2/3)x + 2

You negated the slope but didn't take the reciprocal. Do both: the negative reciprocal of 2/3 is −3/2.

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