What characteristic do slopes of parallel lines share?

Parallel lines are defined by their consistent direction and never intersecting nature, which leads to a critical characteristic: they share the same slope. The slope of a line is the measure of its steepness and direction, and when two lines are parallel, their steepness must be identical.

However, parallel lines can differ in their positions on the graph. This is represented by their y-intercepts, which can vary. The y-intercept is where a line crosses the y-axis, so even though the lines have the same slope, their different y-intercepts ensure that they do not intersect.

The characteristic that encapsulates this relationship is that parallel lines have the same slope but different y-intercepts, making the correct answer a clear representation of this fundamental concept in geometry.