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Unit 2

Introducing Graphs of Proportional Relationships

Introducing Proportional Relationships

Lesson 10

Expressions and Equations

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Let’s see how graphs of proportional relationships differ from graphs of other relationships.

Unit 2 ● Lesson 10

Learning

Goal

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Notice These Points

Unit 2 ● Lesson 10 ● Activity 1

  1. Plot the points (0, 10), (1, 8), (2, 6), (3, 4), and (4, 2).
  2. What do you notice about the graph?

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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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Notice These Points

Unit 2 ● Lesson 10 ● Activity 1

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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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T-shirts for Sale

Unit 2 ● Lesson 10 ● Activity 2

Some T-shirts cost $8 each.

  1. Use the table to answer these questions.
    1. What does x represent?
    2. What does y represent?
    3. Is there a proportional relationship between x and y?
  • Plot the pairs in the table on the coordinate plane.
  • What do you notice about the graph?

x

y

1

8

2

16

3

24

4

32

5

40

6

48

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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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T-shirts for Sale

Unit 2 ● Lesson 10 ● 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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T-shirts for Sale

Unit 2 ● Lesson 10 ● Activity 2

  • Could we buy 0 shirts? 7 T-shirts? 10 T-shirts? Can we buy half of a T-shirt? Would it make sense to connect these points on the graph with a line? Why or why not?
  • Suppose instead of price per shirt, this graph displayed the cost of cherries that are $8 per pound. Given that context, how should we change 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.

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Matching Tables and Graphs

Unit 2 ● Lesson 10 ● Activity 3

Your teacher will give you papers showing tables and graphs.

  1. Examine the graphs closely. What is the same and what is different about the graphs?
  2. Sort the graphs into categories of your choosing. Label each category. Be prepared to explain why you sorted the graphs the way you did.
  3. Take turns with a partner to match a table with a graph.
    1. For each match you find, explain to your partner how you know it is a match.
    2. For each match your partner finds, listen carefully to their explanation. If you disagree, work to reach an agreement.

Pause here so your teacher can review your work.

  • Trade places with another group. How are their categories the same as your group's categories? How are they different?
  • Return to your original place. Discuss any changes you may wish to make to your categories based on what the other group did.
  • Which of the relationships are proportional?
  • What have you noticed about the graphs of proportional relationships? Do you think this will hold true for all graphs of proportional relationships?

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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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Matching Tables and Graphs

Unit 2 ● Lesson 10 ● Activity 3

  • How do you know the relationship is proportional? What have you learned about proportional relationships that applies here?
  • The line for the graph of every proportional relationship will pass through which coordinate point? Why?
  • For which of these situations would you connect the points on the graph with an unbroken line? Why?

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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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Introducing Graphs of Proportional Relationships

Unit 2 ● Lesson 10

  • How will you know if a graph represents a proportional relationship?
  • What are the characteristics of proportional relationships where you can connect the points on the graph with an unbroken line?
  • What are the characteristics of proportional relationships where you cannot connect the points on the graph with a line?
  • What is the mathematical term for the point (0, 0)? Why is this point on the line for every 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.

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Unit 2 ● Lesson 10

I know that the graph of a proportional relationship lies on a line through (0, 0).

Learning

Targets

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Which Are Not Proportional

Unit 2 ● Lesson 10 ● Activity 4

Which graphs cannot represent a proportional relationship? Select all that apply. Explain how you know.

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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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Word:

Coordinate plane

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Definition:

A system for telling where points are located.

Example:

Point R is located at (3,2)

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Word:

Origin

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Definition:

The origin is the point (0,0) in the coordinate plane, where the x-axis and y-axis intersect.

Example:

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Lesson Video

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