Unit 2

Interpreting Graphs of Proportional Relationships

Introducing Proportional Relationships

Lesson 11

Expressions and Equations

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Let’s read stories from the graphs of proportional relationships.

Unit 2 ● Lesson 11

Learning

Goal

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What Could the Graph Represent?

Unit 2 ● Lesson 11 ● Activity 1

Here is a graph that represents a proportional relationship.

1. Invent a situation that could be represented by this graph.
2. Label the axes with the quantities in your situation.
3. Give the graph a title.
4. There is a point on the graph. What are its coordinates? What does it represent in your situation?

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Tyler's Walk

Unit 2 ● Lesson 11 ● Activity 2

Tyler was at the amusement park. He walked at a steady pace from the ticket booth to the bumper cars.

1. The point on the graph shows his arrival at the bumper cars. What do the coordinates of the point tell us about the situation?
2. 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.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Tyler's Walk

Unit 2 ● Lesson 11 ● Activity 2

3. What does the point (0, 0) mean in this situation?
4. 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.
5. 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?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Tyler's Walk

Unit 2 ● Lesson 11 ● Activity 2

• What quantities are shown in the graph?
• How far is the ticket booth from the bumper cars?
• Do the values in your table show a proportional relationship? How do you know?
• What do the coordinates of the points on the graph show?
• What is the equation of this proportional relationship?
• Where do you see k, the constant of proportionality in the table? The graph? The description of the situation?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Seagulls Eat What?

Unit 2 ● Lesson 11 ● Activity 3

1. Plot a point that shows the number of seagulls and the amount of garbage they ate.
2. Use a straight edge to draw a line through this point and (0, 0).
3. Plot the point (1, k) on the line. What is the value of k? What does the value of k tell you about this context?

4 seagulls ate 10 pounds of garbage. Assume this information describes a proportional relationship.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Seagulls Eat What?

Unit 2 ● Lesson 11 ● Activity 3

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Seagulls Eat What?

Unit 2 ● Lesson 11 ● Activity 3

• Does it make sense to try to interpret the meaning of every point on the solid line?
• Why is it still useful to draw the line? How can it help us to learn more about the situation?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Interpreting Graphs of Proportional Relationships

Unit 2 ● Lesson 11

• What can the points on the graph of a proportional relationship tell us about the context it represents?
• What information can you get from the y-value when x = 1 in the table or graph of a proportional relationship?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 2 ● Lesson 11

• I can draw the graph of a proportional relationship given a single point on the graph (other than the origin).
• I can find the constant of proportionality from a graph.
• I understand the information given by graphs of proportional relationships that are made of up of points or a line.

Learning

Targets

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Filling a Bucket

Unit 2 ● Lesson 11 ● Activity 4

Water runs from a hose into a bucket at a steady rate. The amount of water in the bucket for the time it is being filled is shown in the graph.

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1. The point (12, 5) is on the graph. What do the coordinates tell you about the water in the bucket?
2. How many gallons of water were in the bucket after 1 second? Label the point on the graph that shows this information.

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7

Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Lesson Video

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