Question

Are (4/3) and (-3/4) perpendicular lines?

A. Yes
B. No
C. It depends on the slope.
D. It depends on the y-intercept.

Answer 1

The lines with slopes (4/3) and (-3/4) are perpendicular, as their slopes multiply to -1, which satisfies the condition for perpendicular lines. The y-intercept does not affect this relationship.

Step-by-step explanation:

To determine if the lines with slopes (4/3) and (-3/4) are perpendicular, we need to recall the definition of perpendicular lines in the context of slope. Two lines are perpendicular if the product of their slopes is -1. In this case, multiplying the slope of the first line, (4/3), by the slope of the second line, (-3/4), gives us:

(4/3) × (-3/4) = -1

Since the product of the slopes is -1, the lines with these slopes are indeed perpendicular. Therefore, the answer to the student's question is 'Yes'. It does not depend on the y-intercept because perpendicularity is a relationship based solely on the slopes of the lines.