If a line has slope 3, the slope of a line perpendicular to it is which of the following?

• A. -3
• B. 1/3
• C. 3
• D. -1/3

Answer: (D)

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has slope m, a line perpendicular to it has slope -1/m. Here, m = 3, so the perpendicular slope is -1/3. This makes the product 3 × (-1/3) = -1, which is the defining relation for perpendicular slopes (for non-vertical lines). The other options don’t fit: -3 would give a product of -9, not -1; 1/3 is the positive reciprocal and would yield a product of 1, not -1; and 3 would just be parallel, not perpendicular.