Unit 2, Lesson 13
Two Graphs for Each Relationship
Grade 7
13.1
Warm-up
Which three go together? Why do they go together?
Student Lesson Summary
Imagine that a faucet is leaking at a constant rate and that every 2 minutes, 10 milliliters of water leaks from the faucet. There is a proportional relationship between the volume of water and elapsed time.
- We could say that the elapsed time is proportional to the volume of water. The corresponding constant of proportionality tells us that the faucet is leaking at a rate of of a minute per milliliter.
- We could say that the volume of water is proportional to the elapsed time. The corresponding constant of proportionality tells us that the faucet is leaking at a rate of 5 milliliters per minute.
Let’s use to represent volume in milliliters and to represent time in minutes. Here are graphs and equations that represent both ways of thinking about this relationship:
A line graph has a horizontal v-axis and a vertical t-axis. The line begins at the origin and moves upwards and to the right passing through the points with coordinates (1 comma 1/5) and (10 comma 2). The graph is labeled with the equation t = 1/5 v.
A line graph has a horizontal t-axis and vertical v-axis. The line begins at the origin and moves upwards and to the right passing through the points with coordinates (1 comma 5) and (2 comma 10). The graph is labeled with the equation v =5 t.
Even though the relationship between time and volume is the same, we are making a different choice in each case about which variable to view as the independent variable. The graph on the left has as the independent variable, and the graph on the right has as the independent variable.
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