In this lesson, students practice writing two different equations for the same proportional relationship. This is accomplished by switching which quantity is regarded as being proportional to the other. Students see why the constants of proportionality associated with the two equations are reciprocals of each other.

For example, if a person runs at a constant speed and travels 12 miles in 2 hours, then the distance traveled is proportional to the time elapsed, with constant of proportionality 6, because . The time elapsed is proportional to distance traveled with constant of proportionality , because . 

The activities in this lesson use familiar contexts, but not identical situations from previous lessons: measurement conversions and water flowing at a constant rate. Students are expected to use methods developed earlier: organize data in a table, write and solve an equation to determine the constant of proportionality, and generalize from repeated calculations to arrive at an equation (MP8). Students also practice reasoning quantitatively and abstractly as they write or use an equation and then interpret their answers in the context of the situation (MP2). The last activity is optional because it provides an opportunity for additional practice with a new context.