What does it mean for two lines to be parallel?

Two lines are considered parallel when they never intersect and maintain the same slope throughout their lengths. This means that no matter how far you extend the lines in either direction, they will never meet. The consistent slope signifies that they run in the same direction, which is a fundamental property of parallel lines in a two-dimensional plane.

In contrast, other choices suggest relationships between lines that involve them either meeting (which would indicate they are not parallel) or having different angular relationships, such as being perpendicular, which is also not applicable to parallel lines. Thus, the defining characteristic of parallel lines is that they never cross and exhibit the same slope.