Draw a distance vs. time graph to describe the following scenario. Explain your reasoning behind the shape of the graph, especially each time the graph changes its path.
Jack was running late for school, so he had to run the one mile distance from home to school if he was going to get there on time. During the first minute, Jack sprinted out the door and on his way, but then he gradually slowed down during the second minute. The third minute he was so tired from sprinting that he stopped to take a break. Then he realized that he forgot his book and so returned home at a constant jogging pace over the fourth through sixth minutes. When he got home, Jack’s mother was there, and she offered to give him a ride to school. So, during the seventh and eighth minutes, Jack rode in his mom’s car to school (with his mom driving at a constant rate).
What does the average slope in this situation describe?