Lesson 11
Interpreting Graphs of Proportional Relationships
Let’s read stories from the graphs of proportional relationships.
Problem 1
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T024906Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=166dffc9bc51db0d521c2bfc59aa2fe6205f8c6b969ec526cbe0ddd3c879aafd)
- 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 2
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T024906Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5b36c6f37dcafa68f8c8cd3c3c0a33a9964d7f17fc5a2f298ed63cd5915f693d)
Problem 3
To make a friendship bracelet, some long strings are lined up then taking one string and tying it in a knot with each of the other strings to create a row of knots. A new string is chosen and knotted with the all the other strings to create a second row. This process is repeated until there are enough rows to make a bracelet to fit around your friend's wrist.
Are the number of knots proportional to the number of rows? Explain your reasoning.
Problem 4
What information do you need to know to write an equation relating two quantities that have a proportional relationship?