## Representing Data Using Graphs and Tables

In this Gizmo™, a cat is 20 meters from a mouse hole and a mouse is between the cat and its hole. The cat sees the mouse and chases it. Will the cat catch the mouse? Follow the instructions below to find out.

1. Use the Mouse: head start, in meters slider to give the mouse a 6-meter head start, use the Mouse: average speed, in meters per second slider to set the speed of the mouse to 4 meters per second, and use the Cat: average speed, in meters per second slider to set the speed of the cat to 7 meters per second. (To quickly set a slider to a specific number, type the number into the field to the right of the slider, and then press Enter.)
1. At the beginning of this simulation, how far is the mouse from the mouse hole?
2. Will the cat catch the mouse? If so, how far will the cat have to run before it catches the mouse? Check your answer by clicking SIMULATE. Then click Reset.
2. On the x-axis, the graph shows how long each animal has been running, and on the y-axis, the graph shows the distance of each animal from where the cat started. Looking at the graph you'll see that both the cat and mouse run at a constant speed. Therefore, each animal's movement can be modeled as a linear function.
1. What does the slope of a line represent in this situation?
2. What does the y-intercept of a line represent?
3. Select the TABLE view. (Make sure that the mouse's head start is set to 6 meters, the mouse's speed is set to 4 meters per second, and the cat's speed is set to 7 meters per second.) The table shows the location of the cat and mouse after each tenth of a second. For example, if the cat and mouse have been running for 0.3 seconds (t = 0.3), then the mouse is 7.2 meters from the cat's starting point. Verify that the speed of the mouse is constant by performing the following calculations:
1. How far does the mouse run between 0.1 seconds and 0.2 seconds?
2. How far does the mouse run between 0.2 seconds and 0.3 seconds?
3. Are the values the same, or different? Does this match what you see in the graph?
4. Return to the CONTROLS view. Set the mouse's head start to 9 meters (make sure that the mouse's speed is set to 4 meters per second and the cat's speed is set to 7 meters per second) and click SIMULATE.
1. Does the cat catch the mouse? If so, how far does the cat run before catching the mouse?
2. How do you know whether or not the cat catches the mouse by examining the graph?

## Intersecting Lines

1. Set the mouse's head start to 2 meters. Set the speed of the mouse to 6 meters per second, and the speed of the cat to 7 meters per second. Click SIMULATE.
1. How far did the cat have to run to catch the mouse?
2. For how long did the animals run?
3. What is the point where the lines on the graph intersect? To see the coordinates of the point of intersection, turn on Show whether cat catches mouse or place your cursor over the point of intersection on the graph.
4. What can you conclude about the coordinates of that point, in general? Try a few other scenarios by changing some of the sliders, and see if this is always true.
2. Select the TABLE view. (Make sure that the mouse's head start is set to 2 meters, the mouse's speed is set to 6 meters per second, and the cat's speed is set to 7 meters per second.)
1. Which row in the table indicates where the cat catches the mouse?
2. What are the coordinates of the point of intersection of the lines on the graph? Does this correspond to the row you identified in the table?
3. On paper, make a graph that models each of the following situations. (Remember that a head start is the y-intercept of a line, and running speed is the slope of a line.) Does the cat catch the mouse? If it does, estimate how long the chase lasts, and how far the mouse is from its hole when it's caught. Check your work and find exact answers by graphing the system in the Gizmo.
1. The mouse has a 3-meter head start. The cat and mouse both run at 5 meters per second.
2. The mouse has a 5-meter head start, and runs at 6 meters per second. The cat runs at 12 meters per second.
3. The mouse has an 8-meter head start, and runs at 4 meters per second. The cat runs at 7 meters per second.