Rate of change may be represented in various forms. The Williams family is taking a road trip to visit relatives for the holidays. Mrs. Williams drives at an average speed of 60 miles per hour. If Mrs. Williams has been driving for x hours, what is the number of miles, y, that the Williams family has traveled?

Let’s represent this situation using a table, algebraic representation, and a graph.

Move your mouse over the interactive to see the different representations of this situation.

Pause and Reflect

In each representation, what similarities do you see in the changes in distance and changes in time?

Check Your Answer

In the verbal, table, graph, and algebraic representations the change in distance for 1 hour is 60 miles.

Practice

The table below shows the distance and time for the Pennington's family road trip. Use the table to answer questions 1 – 3.

1. What is the rate of change in the table?

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   Determine the ratio of the change in the dependent variable (distance) to the change in the independent variable (time).

   Check Your Answer

   Rate of Change = change in y over change in x Change in y Change in x = 340 miles – 170 miles over 4 hours – 2 hours 340 miles – 170 miles 4 hours – 2 hours = 170 miles over 2 hours 170 miles 2 hours = 85 miles per hour

2. Describe the rate of change between the two variables.

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   Write a sentence relating the distance traveled to each hour driven.
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   Check Your Answer

   For each hour traveled, the distance increases by 85 miles.

3. Click on the graph below to plot the points from the table.

4. How does the rate of change for the Williams family road trip compare to the rate of change for the Pennington family road trip?

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   Which of the two numbers is greater?
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   Check Your Answer

   Williams Family Road Trip
   
   Rate of Change = change in y over change in x Change in y Change in x = 340 miles – 170 miles over 4 hours – 2 hours 120 miles – 60 miles 2 hours – 1 hour = 170 miles over 2 hours 60 miles 1 hour = 60 miles per hour
   
   Pennington Family Road Trip
   
   Rate of Change = change in y over change in x Change in y Change in x = 340 miles – 170 miles over 4 hours – 2 hours 340 miles – 170 miles 4 hours – 2 hours = 170 miles over 2 hours 170 miles 2 hours = 85 miles per hour
   

5. How do the graphs of the Williams family road trip and the Pennington family road trip compare?

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   Graph both relationships on the same set of axes, and compare the two lines.
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   Check Your Answer

   The graph of the data for the Pennington family road trip is steeper than the graph of the data for the Williams family road trip.