Final answer:
On a distance vs. time graph, the line of an object at rest is a horizontal line, indicating that the displacement stays constant over time because there is no change in the position of the object.
Step-by-step explanation:
On a distance vs. time graph, the line representing an object at rest is a horizontal line. This indicates that there is no change in the position of the object over time, hence the displacement remains constant. The equation of a straight line, as mentioned in the context, is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. For an object at rest, the 'm' (slope) would be zero since there is no change in distance, regardless of the time elapsed. Thus, the graph would show a straight horizontal line indicating the object's constant position over the time interval.
If we look at the graph of Position vs. Time knowing that 'a' (acceleration) equals 0 and 'v' (velocity) is constant, it can be inferred that if an object is not moving, its velocity is 0. This further confirms that on a position vs. time graph, an object at rest will have a horizontal line reflecting no change in position. When an object's position doesn't change over time, it translates to a lack of displacement, and therefore, the object is at rest or stationary.
Taking into account the acceleration vs. time graph, for an object at rest, this would also be a horizontal line at the zero value, since at rest, there is no change in velocity, and acceleration is the rate at which velocity changes over time.