Unit 2, Lesson 13
Two Graphs for Each Relationship
Grade 7
13.1
Warm-up
Which Three Go Together: Graphs
Which three go together? Why do they go together?
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Which three go together? Why do they go together?
Your teacher will assign you one of these three points:
Use your graph to find the
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Your teacher will give you a completed table. Use it to check your values.
Choose three rows, other than the row that represents the origin, from the completed table. Record the values and compute
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What is the
Compare your representations with the rest of your group. Discuss what is the same and what is different about:
Andre and Jada had a contest making balloon animals.
Here are two different graphs that both represent this situation.
A graph on a coordinate plane. The graph has two points. The horizontal axis is labeled "time in minutes" and the vertical axis is labeled "number of balloon animals." The first point is to the right of the vertical axis and high above the horizontal axis. The second point is to the right and above the first point.
A graph on a coordinate plane. The graph has two points. The horizontal axis is labeled "number of balloon animals" and the vertical axis is labeled "time in minutes." The first point is far to the right of the vertical axis and above the horizontal axis. The second point is to the right and above the first point.
On the first graph, which point shows Andre’s work and which shows Jada’s work? Label them.
Draw two lines: one through the origin and Andre’s point, and one through the origin and Jada’s point.
Write an equation for each line. Use
Andre:
Jada:
For each equation, what does the constant of proportionality tell you?
Repeat the previous steps for the second graph.
Andre:
Jada:
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.
Let’s use
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
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