When graphing motion the steepness of the slope depends on what
I want to say that it depends upon the speed/rate that an object is traveling but I no longer have the book to double check myself.
When graphing motion, the steepness of the slope depends on the speed or velocity of the object. The steeper the slope, the faster the object is moving. In other words, the rate at which the object is changing its position determines the steepness of the slope on a motion graph. For example, a steeper slope on a distance-time graph indicates a higher speed, while a steeper slope on a velocity-time graph represents a greater acceleration.
When graphing motion, the steepness of the slope depends on the speed of the object.
To understand why this is the case, let's consider a basic position vs. time graph. In this graph, the vertical axis represents the position of the object, while the horizontal axis represents time.
If the object is not moving and its position remains constant, the graph would be a horizontal straight line, indicating a slope of zero. This means that the speed of the object is zero, and the slope of the graph reflects this lack of motion.
However, if the object is in motion and its position is changing over time, the graph will show a non-zero slope. The steeper the slope, the faster the object is moving. This is because the slope of the graph represents the change in position per unit of time, which is the definition of speed or velocity.
Mathematically, slope is calculated by dividing the change in the vertical coordinate (position) by the change in the horizontal coordinate (time) between two points on the graph. Therefore, the greater the change in position for a given change in time, the steeper the slope of the graph and the faster the object is moving.