Unit 2, Lesson 11
Interpreting Graphs of Proportional Relationships
Grade 7
11.1
Warm-up
Here is a graph that represents a proportional relationship.
Invent a situation that could be represented by this graph.
- Label the axes with the quantities in your situation.
- Give the graph a title.
- There is a point on the graph. What does it represent in your situation?
11.2
Activity
Tyler was at the amusement park. He walked at a steady pace from the ticket booth to the bumper cars.
-
The point on the graph shows his arrival at the bumper cars. What do the coordinates of the point tell us about the situation?
- The table representing Tyler's walk shows other values of time and distance. Complete the table. Next, plot the pairs of values on the grid.
- What does the point mean in this situation?
- How far away from the ticket booth was Tyler after 1 second? Label the point on the graph that shows this information with its coordinates.
- What is the constant of proportionality for the relationship between time and distance? What does it tell you about Tyler's walk? Where do you see it in the graph?
Graph of a point, coordinate plane with grid, origin O. Horizontal axis, elapsed time (seconds), vertical axis, distance from the ticket booth (meters), both have scale 0 to 60 by 10’s. Point at (40 comma 50).
| time (seconds) |
distance (meters) |
|---|---|
| 0 | 0 |
| 20 | 25 |
| 30 | 37.5 |
| 40 | 50 |
| 1 |
Student Lesson Summary
For the relationship represented in this table, is proportional to . We can see in this table that is the constant of proportionality because it’s the value when is 1.
The equation also represents this relationship.
| 4 | 5 |
| 5 | |
| 8 | 10 |
| 1 |
Here is the graph of this relationship.
Graph of a lin, x y plane, origin O. Horizontal and vertical axis scale 0 to 10 by 1’s. Line starts at (0 comma 0), rises to point (1 comma the fraction 5 over 4), rises to point (4 comma 5), rises to point (5 comma the fraction 25 over 4), then rises to point (8 comma 10) and keeps rising.
If represents the distance in feet that a snail crawls in minutes, then the point tells us that the snail can crawl 5 feet in 4 minutes.
If represents the cups of yogurt and represents the teaspoons of cinnamon in a recipe for fruit dip, then the point tells us that you can mix 4 teaspoons of cinnamon with 5 cups of yogurt to make this fruit dip.
We can find the constant of proportionality by looking at the graph: is the -coordinate of the point on the graph where the -coordinate is 1. This could mean the snail is traveling feet per minute or that the recipe calls for cups of yogurt for every teaspoon of cinnamon.
In general, when is proportional to , the corresponding constant of proportionality is the -value when .
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