Two non-parallel lines intersect at how many points?

Two non-parallel lines intersect at how many points?

• A. No solution
• B. The lines are parallel
• C. One solution
• D. The lines are the same line

Answer: (C)

Two lines that aren’t parallel must cross each other in exactly one place on the plane. This happens because their slopes are different, so there is a unique point where their equations line up on both coordinates. If lines were parallel, they wouldn’t meet at all, and if they were the same line, they would meet at infinitely many points. Since these lines are different but not parallel, they intersect at exactly one point.

Two lines that aren’t parallel must cross each other in exactly one place on the plane. This happens because their slopes are different, so there is a unique point where their equations line up on both coordinates. If lines were parallel, they wouldn’t meet at all, and if they were the same line, they would meet at infinitely many points. Since these lines are different but not parallel, they intersect at exactly one point.