Which statement correctly characterizes parallel lines?

• A. Their slopes are equal.
• B. Their slopes are negative reciprocals.
• C. They intersect at a right angle.
• D. Their slopes are reciprocals but opposite signs.

Answer: (A)

Parallel lines move in the same direction and never cross, which in algebra means they share the same rate of change, or slope. When two lines have equal slopes, they rise and run the same amount over any horizontal distance. If their intercepts are different, they never meet, so they are parallel. The other ideas describe perpendicular relationships: negative reciprocal slopes produce lines that intersect at a right angle, and saying slopes are reciprocals with opposite signs is another way to describe that perpendicularity. A special case is vertical lines, which have undefined slopes, but they’re still parallel if they point straight up and down together. So, equal slopes best capture the idea of parallel lines.