Recently, Kalani and Lynette took a trip in California from Vacaville to Los Angeles. The graph at right represents their trip.

1. Explain what each line segment in the graph represents.

   Hint (a):

   Are they traveling at the same speed all throughout the trip?

   Answer (a):

   A portion of the trip at a specific speed.

2. About how many miles is it from Vacaville to Los Angeles? How do you know?

   Hint (b):

   Which axis represents distance (measured in miles)?

   Answer (b):

   About $400$ miles.

3. Using the graph shown above, sketch a graph that would represent their speed while traveling. Take your time to think this through carefully and be sure to label the axes.

   Hint (c):

   To find the speed in miles per hour for a portion of the trip, divide the number of miles traveled in that portion by the number of hours it took to travel that portion.

   Answer (c):

   Graph shown below—a speed of approximately $30$ mph for $1$ hour, approximately $80$ mph for the next $3$ hours, $0$ mph for $2$ hours, approximately $40$ mph for $2$ hours, and then approximately $20$ mph for the last $2$ hours. Note that the step graph assumes instantaneous change of speed, which is not technically possible.