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Unit 2

Two Graphs for Each Relationship

Introducing Proportional Relationships

Lesson 13

Expressions and Equations

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Let’s use tables, equations, and graphs to answer questions about proportional relationships.

Unit 2 ● Lesson 13

Learning

Goal

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Fractions and Decimals

Unit 2 ● Lesson 13 ● Activity 1

Decide whether each equation is true or false. Be prepared to explain your reasoning.

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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.

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Tables, Graphs, and Equations

Unit 2 ● Lesson 13 ● Activity 2

Your teacher will assign you one of these three points: A = (10, 4), B = (4, 5), C = (8, 5)

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  1. On the graph, plot and label only your assigned point.
  2. Use a ruler to line up your point with the origin, (0, 0). Draw a line that starts at the origin, goes through your point, and continues to the edge of the graph.
  3. Complete the table with the coordinates of points on your graph. Use a fraction to represent any value that is not a whole number.

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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.

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Tables, Graphs, and Equations

Unit 2 ● Lesson 13 ● Activity 2

  1. Write an equation that represents the relationship between x and y defined by your point.
  2. Compare your graph and table with the rest of your group. What is the same and what is different about:
    1. your tables?
    2. your equations?
    3. your graphs?
  3. What is the y-coordinate of your graph when the x-coordinate is 1? Plot and label this point on your graph. Where do you see this value in the table? Where do you see this value in your equation?
  4. Describe any connections you see between the table, characteristics of the graph, and the equation.

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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.

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Tables, Graphs, and Equations

Unit 2 ● Lesson 13 ● Activity 2

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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.

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Tables, Graphs, and Equations

Unit 2 ● Lesson 13 ● Activity 2

  • A graph of a line through the origin and passing through the first quadrant represents what kind of relationship?
  • What does computed from any point (a, b) on the line represent?
  • What is the equation for the line and the relationship where k is for any point (a, b) on the graph other than the origin?

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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.

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Hot Dog Eating Contest

Unit 2 ● Lesson 13 ● Activity 3

Andre and Jada were in a hot dog eating contest. Andre ate 10 hot dogs in 3 minutes. Jada ate 12 hot dogs in 5 minutes.

Here are two different graphs that both represent this 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.

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Hot Dog Eating Contest

Unit 2 ● Lesson 13 ● Activity 3

  1. On the first graph, which point shows Andre’s consumption and which shows Jada’s consumption? Label them.
  2. Draw two lines: one through the origin and Andre’s point, and one through the origin and Jada’s point.
  3. Write an equation for each line. Use to represent time in minutes and to represent number of hot dogs.
    1. Andre:
    2. Jada:
  4. For each equation, what does the constant of proportionality tell you?
  5. Repeat the previous steps for the second graph.
    • Andre:
    • Jada:

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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.

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Hot Dog Eating Contest

Unit 2 ● Lesson 13 ● 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.

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Two Graphs for Each Relationship

Unit 2 ● Lesson 13

  • Do the graphs and the equations tell the same story?
  • How can you see the same information in both?

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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.

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Unit 2 ● Lesson 13

  • I can interpret a graph of a proportional relationship using the situation.
  • I can write an equation representing a proportional relationship from a graph.

Learning

Targets

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Spicy Popcorn

Unit 2 ● Lesson 13 ● Activity 4

Elena went to a store where you can scoop your own popcorn and buy as much as you want. She bought 10 ounces of spicy popcorn for $2.50.

  1. How much does popcorn cost per ounce?
  2. How much popcorn can you buy per dollar?
  3. Write two different equations that represent this situation. Use p for ounces of popcorn and c for cost in dollars.
  4. Choose one of your equations, and sketch its graph. Be sure to label the axes.

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Cool-down

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

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Lesson Video

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