What characteristic is true for the slopes of parallel lines?

For parallel lines, the defining characteristic of their slopes is that they are equal. Parallel lines run in the same direction and will never intersect, which is only possible if their slopes maintain the same value. This means that for any linear equation representing a parallel line, the coefficient of the x-term (which represents the slope) remains constant regardless of the specific y-intercept.

In contrast, changing slopes would indicate that the lines are not maintaining the same direction, while differing slopes suggest that the lines would eventually meet or intersect at some point. On the other hand, having opposite slopes would imply that the lines meet at a right angle, which contradicts the essential nature of parallel lines. This is why stating that the slopes of parallel lines are equal accurately captures their relationship in geometric terms.