This lesson using InspireData provides middle/high students with a real-life example of linear growth and systems of linear equations. Students will analyze data about gym membership costs and decide which gym is the most affordable. Optionally, they can write equations for each line and use these to practice solving systems of equations.

• Based on the table, have students write a short advertising statement for each gym. For example, “At Muscle World, join for only $100 and pay $40 per month.”
• Switch over to Plot View and run the time series for Month vs. Total Cost. Play it all at once, and then month by month using the Series Display controls. Solicit answers to the questions below:
For which gym are costs growing at the slowest rate (or fastest)?
What does a point of intersection mean in the context of the situation?
Which gym is the most affordable at the following points in time:
-when the member joins?
-after 4 months of payments?
-after 6 months of payments?
-after 8 months of payments?
-after 10 months of payments?
-after 12 months of payments?
-after 14 months of payments?
-after 16 months of payments?
-after 18 months of payments?
• Based on the table and graph, write an equation for each gym’s total cost.
• Use the equations to verify costs at intersection points or any other points in time.
• Ask students to decide which gym they would join, assuming quality was the same at each gym. Why might someone decide to join Fitness Land despite a higher cost in the long run?
• As a class or individually, have students make up a second situation involving linear growth in the provided table.

This activity was created using InspireData 1.5, which must be installed to open the file. Download a 30-day free trial at href="http://www.inspiration.com/freetrial">www.inspiration.com/freetrial or if you have InspireData 1.0, download a complementary upgrade.