Final answer:
Perpendicular lines have slopes with opposite signs because they intersect at a right angle.
Step-by-step explanation:
Perpendicular lines are lines that intersect at a right angle or 90 degrees. The slopes of perpendicular lines have opposite signs because their angles are complementary, meaning they add up to 90 degrees. If one line has a positive slope, the other line will have a negative slope, and vice versa.
For example, if Line A has a slope of 2, Line B (perpendicular to Line A) will have a slope of -1/2. If Line A has a slope of -3, Line B will have a slope of 1/3.