Two distinct lines in a plane share the same slope and never meet. What term describes these lines?

• A. Parallel
• B. Similar
• C. Perpendicular
• D. Intersecting

Answer: (A)

Same slope means the lines rise and run at the same rate. If two distinct lines share that rate, they either are the same line or run side by side without ever crossing. The term for the latter situation is parallel lines. You can see this with equations: y = m x + b1 and y = m x + b2. If the intercepts differ (b1 ≠ b2), setting the equations equal to find an intersection gives m x + b1 = m x + b2, which simplifies to b1 = b2—impossible when b1 ≠ b2. So there is no intersection, which is exactly what parallel lines do. For example, y = 2x + 1 and y = 2x - 3 share slope 2 but never meet.