Curriculum  /  Math  /  8th Grade  /  Unit 5: Linear Relationships  /  Lesson 14

Linear Relationships

Lesson 14

Math

Unit 5

8th Grade

Lesson 14 of 15

Objective

Compare linear functions represented in different ways.

Common Core Standards

Core Standards

  • 8.F.A.2 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
  • 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.

Criteria for Success

  1. Identify slope and $$y$$-intercept of lines represented as graphs, tables, and equations.
  2. Compare the slopes and $$y$$-intercepts of linear functions. 

Tips for Teachers

In Lessons 9 and 10 of Unit 4, students compared functions by looking at the rates of change and initial values of those functions. This lesson revisits some of those concepts, but looks specifically at linear functions and describes the graphs of these functions by the slope and $$y$$-intercept of the line. 

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

Three linear functions are represented below.

Function A: Function B: Function C:
$$y=x$$

$$x$$ $$y$$
-3 1
6 4
9 5

 

a.   Order the functions by the slope of the line that represents each function, from least to greatest.

b.   Order the functions by the $$y$$-intercept of the line that represents each function, from least to greatest.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

Three friends participate in the loyalty program at a local coffee shop. A participant in the program earns points for each visit that can be used to get drinks and food for free. The graph below shows the point balances of the three friends over several weeks. 

a.   Describe what each line tells you about the friends’ point balance. What can you tell about how they earn and use their points? 

b.   Who has the most points at the start? 

c.   Write an equation for the point balance for each friend. 

d.   A fourth friend has a point balance represented by the equation $${y=12x+50}$$. Does this friend earn points at a faster or slower rate than Adan?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 3

Line $$L$$ goes through the points (4, 9) and (-4, -7). Line $$M$$ has a $$y-$$intercept that is greater than line $$L$$.

What could be the equation for line $$M$$?

Create a free account or sign in to view multiple choice options

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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

Linear function $$K$$ is represented by the equation $${y={1\over2}x-2}$$.

Draw the graph of a line that has a greater slope than function $$K$$ and the same $$y$$-intercept as function $$K$$.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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 multiple-choice problems where students are presented with two linear functions and determine true statements that compare slope and/or $$y$$-intercepts of the lines.
  • MARS Formative Assessment Lesson for Grade 8 Comparing Lines and Linear Equations — Great activity where students are required to pay close attention to how graphs and equations represent different rates.
  • EngageNY Mathematics Grade 8 Mathematics > Module 5 > Topic A > Lesson 7 — Revisit the Problem Set; this was included as a resource in Unit 4 Lesson 9 but may be worthwhile returning to in light of the new concepts learned in this unit.

Next

Model real-world situations with linear relationships.

Lesson 15
icon/arrow/right/large

Lesson Map

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

Topic A: Comparing Proportional Relationships

Topic B: Slope and Graphing Linear Equations

Topic C: Writing Linear Equations

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free