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

Linear Relationships

Lesson 5

Math

Unit 5

8th Grade

Lesson 5 of 15

Objective

Graph a linear equation using a table of values.

Common Core Standards

Core Standards

  • 8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Foundational Standards

  • 6.EE.C.9
  • 7.RP.A.2

Criteria for Success

  1. Create a table of values from an equation to represent solutions to the equation, using a variety of values for $$x$$ including positives, negatives, and zero where applicable.
  2. Use a table of values to graph a linear equation, understanding that the points connect together to form a straight line. 
  3. Graph linear equations in all four quadrants of the coordinate plane. 
  4. Understand that solutions to the equation or situation can be represented in both the table of values and on the line in the graph.

Tips for Teachers

In Lesson 5, students begin to venture beyond proportional relationships and explore linear functions in all four quadrants of the coordinate plane with positive and negative slopes. They start by graphing linear equations using a table of values, a valuable skill for graphing that students had some exposure to in Unit 4 Lesson 7, as well as in prior grade levels with proportional relationships. In the lessons to follow, students will investigate slope and the $$y$$-intercept to find more efficient ways to graph linear equations. 

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Anchor Problems

25-30 minutes

Problem 1

After a house was built, it starts to settle into the ground. Its elevation starts at sea level, and the house sinks $$\frac{1}{2}$$ cm each year. 

a.   Write a function to represent the elevation of the house, $$y$$, in cm after $$x$$ years.

b.   Create a table of values for the function with at least 5 values of $$x$$ and $$y$$.

c.   Use the table of values to graph the relationship.

Guiding Questions

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Student Response

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Problem 2

Emily tells you that she scored 18 points in a basketball game. 

a.   Write down all the possible ways she could have scored 18 points with only two- and three-point baskets. Use the table below to organize your work. 

Number of Two-Point Baskets Number of Three-Point Baskets
   
   
   
   

b.   Write an equation to represent the situation, with $$x$$ as the number of two-point baskets and $$y$$ as the number of three-point baskets Emily scored. Then graph the situation. 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic B > Lesson 12 — Opening Exercise

Grade 8 Mathematics > Module 4 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Find five solutions for the linear equation $${y=2x-10}$$ to create a table of values. Use a variety of values for $$x$$. Plot the points and graph the situation on the coordinate plane. 

$$x$$ $$y$$
   
   
   
   
   

 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic B > Lesson 12 — Exploratory Challenge #2

Grade 8 Mathematics > Module 4 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

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

Problem 1

Is the point ($$6$$, $$-1$$) a solution to the linear equation $$-2x + 4y = -8$$? Explain.

Student Response

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Problem 2

Find three solutions to the linear equation $$2x + 4y = -12$$ and use them to graph the equation.

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.

  • Include problems where students are given a linear equation and are asked to create a table of values in order to graph the equation. Include a mix of proportional and non-proportional relationships with positive and negative slopes. 

Next

Define slope and determine slope from graphs.

Lesson 6
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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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