The purpose of this discussion is to introduce students to the term “rate of change.” Begin by inviting 2–3 students to share the graphs they created. Emphasize how different scales can be used, but in order to be helpful, the scale for the number of cars, , on the horizontal axis should extend to at least 23 and the scale for the amount raised in dollars, , on the vertical axis should extend to at least 200.

Next, tell students that an equation that represents this situation is , where is the number of cars, and is the total dollars raised. Display this equation for all to see, then discuss:

• “What is the constant of proportionality and what does it mean?” (The constant of proportionality is 8.5 and it means that each car washed raised $8.50.)

• “How can you see the constant of proportionality in the graph and the table? (Graph: The slope of the line is equivalent to 8.5. Table: For any given row, the amount raised in dollars divided by the number of cars washed equals 8.5.)

• “Which representation do you think is more useful when calculating the constant of proportionality? Why?”

Explain that the constant of proportionality can be thought of as the rate of change: the amount one variable changes by when the other variable increases by 1. In the case of the Origami Club’s car wash, the rate of change of , the amount they raise in dollars, with respect to , the number of cars they wash, is 8.50 dollars per car.

If students are unsure how to scale the axes on their graphs, consider asking:

• “What are the largest values that need to be shown on the graph?”

• “How many grid lines are there?”