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Interpreting Graphs of Proportional Relationships


Videos to help Grade 7 students learn how to interpret graphs of proportional relationships.

New York State Common Core Math Grade 7, Module 1, Lesson 10.

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New York State Common Core Math Grade 7, Module 1, Lesson 10

Lesson 10 Student Outcomes

Students consolidate their understanding of equations representing proportional relationships as they interpret what points on the graph of a proportional relationship mean in terms of the situation or context of the problem, including the point (0, 0)

Students are able to identify and interpret in context the point (1, r) on the graph of a proportional relationship where is the unit rate.

Lesson Summary:

The points (0, 0) and (1, r), where r is the unit rate, will always fall on the line representing two quantities that are proportional to each other.

The unit rate r in the point (1, r) represents the amount of vertical increase for every horizontal increase of 1 unit on the graph.

The point (0, 0) indicates that when there is zero amount of one quantity, there will also be zero amount of the second quantity.

These two points may not always be given as part of the set of data for a given real-world or mathematical situation, but they will always fall on the line that passes through the given data points.

Example 1

Grandma’s Special Chocolate-Chip Cookie recipe, which yields 4 dozen cookies, calls for 3 cups of flour to make 4 dozen cookies. Using this information, complete the chart:
Table – Create a chart comparing the amount of flour used to the amount of cookies.
Table – Is the number of cookies proportional to the amount of flour used? Explain.
Unit Rate – What is the unit rate, and what is the meaning in the context of the problem?
Graph – Model the relationship on a graph.
Does the graph show the two quantities being proportional to each other? Explain.
Equation – Write an equation that can be used to represent the relationship.

Example 2

Below is a graph modeling the amount of sugar required to make Grandma’s Chocolate-Chip Cookies.
Record the coordinates of flour of the points from the graph in a table. What do these ordered pairs (values) represent?
Grandma has 1 remaining cup of sugar, how many dozen cookies will she be able to make? Plot the point on the graph above.
How many dozen cookies can grandma make if she has no sugar? Can you graph this on the grid provided above? What do we call this point?


1. The graph below shows the amount of time a person can shower with a certain amount of water.
a. Can you determine by looking at the graph whether the length of the shower is proportional to the number of gallons of water? Explain how you know.
b. How long can a person shower with 15 gallons of water and with 60 gallons of water?
c. What are the coordinates of point A? Describe point A in the context of the problem.
d. Can you use the graph to identify the unit rate?
e. Plot the unit rate on the graph. Is the point on the line of this relationship?
f. Write the equation to represent the relationship between the number of gallons used and the length of a shower.
2. Your friend uses the equation to find the total cost of P people entering the local Amusement Park.
a. Create a table and record the cost of entering the amusement park for several different-sized groups of people.
b. Is the cost of admission proportional to the amount of people entering the Amusement Park? Explain why or why not.
c. What is the unit rate, and what does it represent in the context of the situation?
d. Sketch a graph to represent this relationship.
e. What point(s) MUST be on the graph of the line if the two quantities represented are proportional to each other? Explain why and describe this point in the context of the problem.
f. Would the point be on the graph? What does this point represent in the context of the situation?

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