Lesson 7
Graphs of Proportional Relationships
Let's see how graphs of proportional relationships differ from graphs of other relationships.
Problem 1
A lemonade recipe calls for \(\frac14\) cup of lemon juice for every cup of water.
- Use the table to answer these questions.
- What does \(x\) represent?
- What does \(y\) represent?
- Is there a proportional relationship between \(x\) and \(y\)?
- Plot the pairs in the table in a coordinate plane.
\(x\) | \(y\) |
---|---|
1 | \(\frac14\) |
2 | \(\frac12\) |
3 | \(\frac34\) |
4 | 1 |
Problem 2
There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is $47.94. The point \((6, 47.94)\) is shown on the graph below.
![Graph of a point on a coordinate plane, origin O.](https://cms-im.s3.amazonaws.com/x3gxtTBP54o6p7gLYnSV2GpZ?response-content-disposition=inline%3B%20filename%3D%227-7.2.E.PP.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.E.PP.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T032401Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e9c0bbe834802274d38ad5072f5dc1523d37048d5ffd6e458e6df7f9d5efa525)
- What is the constant of proportionality in this relationship?
- What does the constant of proportionality tell us about the situation?
- Add at least three more points to the graph and label them with their coordinates.
- Write an equation that represents the relationship between \(C\), the total cost of the subscription, and \(m\), the number of months.
Problem 3
The graph shows the amounts of almonds, in grams, for different amounts of oats, in cups, in a granola mix. Label the point \((1, k)\) on the graph, find the value of \(k\), and explain its meaning.
![Line graph. Horizontal axis, oats, cups, 0 to 5, by 1's. Vertical axis, almonds, grams, 0 to 110, by 10's.](https://cms-im.s3.amazonaws.com/ym9ZaHgXhb7HAam6xKDD8a4Z?response-content-disposition=inline%3B%20filename%3D%227-7.2.D11.Image.Revision.128.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.D11.Image.Revision.128.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T032401Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=08131cb7206c132f18d584a21a225e94ffc935f6b3f32fe7ddf9927bb07a1a2f)
Problem 4
Select all the pieces of information that would tell you \(x\) and \(y\) have a proportional relationship. Let \(y\) represent the distance in meters between a rock and a turtle's current position and \(x\) represent the time in minutes the turtle has been moving.
\(y = 3x\)
After 4 minutes, the turtle has walked 12 feet away from the rock.
The turtle walks for a bit, then stops for a minute before walking again.
The turtle walks away from the rock at a constant rate.
Problem 5
What information do you need to know to write an equation relating two quantities that have a proportional relationship?