Question

Determining If Two Lines Are Perpendicular

Are the lines perpendicular?

no, because the slopes of the lines are equal
no, because the slopes of the lines are not opposite reciprocals
yes, because the slopes of the lines are equal
yes, because the slopes of the lines are opposite reciprocals

Answer 1

Correct choice: "yes, because the slopes of the lines are opposite reciprocals."

Reason: Two nonvertical lines with slopes m1 and m2 are perpendicular iff m1·m2 = −1 (i.e., m2 = −1/m1). Equal slopes mean the lines are parallel, not perpendicular. (A vertical line and a horizontal line are perpendicular: one slope is undefined and the other is 0.)