Final answer:
On a graph, a steeper slope indicates that one line represents a faster speed or rate of change. The line with the steeper slope, whether it is increasing or decreasing, is changing at a faster rate than the other line with the less steep slope.
Step-by-step explanation:
If both lines start at the same place on a graph and one is moving faster than another, the line representing the faster movement will have a greater slope than the line with slower movement. In other words, a steeper slope depicts greater speed or rate of change.
When comparing line A and line B from the information provided, if line B is steeper than line A, it means that the movement or rate (velocity if we are discussing a distance versus time graph, or acceleration if it's a velocity versus time graph) represented by line B is faster than that of line A.
Velocity is represented on a distance versus time graph as the slope. So, if we had a graph of position against time, the slope at any point on that graph would represent the instantaneous velocity at that point. Carrying this one step further, on a velocity versus time graph, the slope represents acceleration.
If line A is a decreasing line, this means that it's either moving in the opposite direction or slowing down, depending on whether we're talking about position or velocity.
If line B's slope is increasingly positive, that means it's speed or rate is increasing faster compared to line A. The same concepts apply to negative slopes; a more negative slope represents faster movement in the negative direction or faster deceleration.