Curriculum  /  Math  /  8th Grade  /  Unit 5: Linear Relationships  /  Lesson 2

Linear Relationships

Lesson 2

Math

Unit 5

8th Grade

Lesson 2 of 15

Objective

Graph proportional relationships and interpret slope as the unit rate.

Common Core Standards

Core Standards

  • 8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Foundational Standards

  • 6.EE.C.9
  • 7.RP.A.2

Criteria for Success

  1. Draw graphs for proportional relationships in the coordinate plane. 
  2. Identify the slope of the graph and interpret it in context as the unit rate of the situation. 

Tips for Teachers

Lesson Materials

  • Graph Paper (2-3 sheets per student)
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Anchor Problems

25-30 minutes

Problem 1

At a market, long-grain rice can be purchased in any weight, measured in pounds. The cost and weight are proportional, for example, 5 pounds of rice costs $4.

a.   Write an equation to represent the cost, $$y$$, to purchase $$x$$ pounds of long-grain rice.

b.   Determine the cost of 1, 10, and 15 pounds of rice.

c.   Graph the relationship between cost and weight of rice in the coordinate plane.

d.   What is the slope of the graph? What does it mean as a unit rate?

Guiding Questions

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Student Response

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Problem 2

Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water. 

  • Nia mixed 1 teaspoon salt with 3 cups water.
  • Trey mixed $${1\over 2}$$ teaspoon salt with 1$${{1\over2}}$$cups of water. 

Nia tasted Trey’s salt water. She said,
“I added more salt so I expected that mine would be more salty, but they taste the same.”

a.   Explain why the salt water mixtures taste the same.

b.   Find an equation that relates $$s$$, the number of teaspoons of salt, with $$w$$, the number of cups of water, for both of these mixtures.

c.   Draw the graph of your equation from part (b).

d.   Your graph in part (c) should be a line. Interpret the slope as a unit rate.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Sore Throats, Variation 2

Sore Throats, Variation 2, accessed on Feb. 23, 2018, 11:02 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

At the grocery store, sliced turkey deli meat is on sale for $11 for 2 pounds.

a.   What is the cost per pound of sliced turkey deli meat?

b.   Write an equation to represent the cost, $$y$$, of sliced turkey deli meat measured in $$x$$ pounds.

c.   Draw a graph of the situation.

d.   What is the meaning of the slope of the line that you drew? 

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Compare proportional relationships represented as graphs.

Lesson 3
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Comparing Proportional Relationships

Topic B: Slope and Graphing Linear Equations

Topic C: Writing Linear Equations

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