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MAFS.8.F.1.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

General Information

Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Functions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Define, evaluate, and compare functions. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

Test Item Specifications


  • Assessment Limits :

    Function notation may not be used.

  • Calculator :

    Yes

  • Context :

    Allowable

Sample Test Items (4)

  • Test Item #: Sample Item 1
  • Question:

    Several functions represent different savings account plans.

    Which functions are nonlinear?

  • Difficulty: N/A
  • Type: MS: Multiselect

  • Test Item #: Sample Item 2
  • Question: Jared puts 20 cents in a jar. The following week, he puts two times that original amount in the jar. For each of the following six weeks, Jared continues to double the amount of money he places in his savings jar each week. 

    Determine if the relationship is linear or nonlinear. Explain your choice using examples with ordered pairs.

  • Difficulty: N/A
  • Type: OR: Open Response

  • Test Item #: Sample Item 3
  • Question:

    The function y = 3.50x + 2 represents the total amount of money, y, saved over x weeks.

    What is true about the function?

  • Difficulty: N/A
  • Type: MC: Multiple Choice

  • Test Item #: Sample Item 4
  • Question:

    Kayden creates a linear function where x is the input, y is the output, and m and b are constants.

    A. Which equation could represent Kayden's function?

    B. Which statement about the graph of Kayden's function is true for all values of m and b?

  • Difficulty: N/A
  • Type: SHT: Selectable Hot Text

Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1204000: M/J Intensive Mathematics (MC) (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.8.F.1.AP.3a: Identify graphed functions as linear or not linear.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 4 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 3 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 2 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 1 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Formative Assessments

What Am I?:

Students are asked to describe a linear function, its graph, and the meaning of its parameters.

Type: Formative Assessment

Nonlinear Functions:

Students are asked to provide an example of a nonlinear function and explain why it is nonlinear.

Type: Formative Assessment

Linear or Nonlinear?:

Students are asked to identify a function as either linear or nonlinear and to justify their decision.

Type: Formative Assessment

Explaining Linear Functions:

Students are asked to describe defining properties of linear functions.

Type: Formative Assessment

Lesson Plans

Beginning Linear Functions:

This is a simple lesson used to describe the concept of slope to algebra students. Students will be able to:

  • determine positive, negative, zero, and undefined slopes by looking at graphed functions.
  • determine x- and y- intercepts by substitution or by examining graphs.
  • write equations in slope-intercept form and make graphs based on slope/y-intercept of linear functions.

Type: Lesson Plan

Functions: Are They Linear or Non-Linear?:

In this lesson, students will investigate 5 different functions to see if they are linear or non-linear. They will then analyze the functions in groups. After that they will present their results and reasoning.

Type: Lesson Plan

Original Student Tutorial

Summer of FUNctions:

Have some fun with FUNctions!  Learn how to identify linear and non-linear functions in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

Slope and Deep Sea Sharks:

Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorials

Recognizing Linear Functions:

In this video, you will determine if the situation is linear or non-linear by finding the rate of change between cooordinates. You will check your work by graphing the coordinates given.

Type: Tutorial

Slope-Intercept Form from a Table:

In this video, you will practice writing the slope-intercept form for a line, given a table of x and y values.

Type: Tutorial

Finding the x and y intercepts from an equation:

Students will learn how to find and graph the x and y intercepts from an equation written in standard form.

Type: Tutorial

Graphing x and y intercepts from an equation:

Students will learn how to find the x and y intercepts from an equation in standard form.

Type: Tutorial

Finding intercepts from a table:

This tutorial shows students how to find the y inercept from a table.

Type: Tutorial

Slope-Intercept Equation from Two Solutions:

Given two points on a line, you will find the slope and the y-intercept. You will then write the equation of the line in slope-intercept form.

Type: Tutorial

Graphing a linear equation using a table:

Students will learn how to graph a linear equation using a table. Students will not be required to graph from slope-intercept form, although they will convert the equation from standard form to slope-intercpet form before they create the table.

Type: Tutorial

Graph a line in slope-intercept form:

This tutprial shows how to graph a line in slope-intercept form.

Type: Tutorial

Dependent and independent variables exercise: graphing the equation:

It's helpful to represent an equation on a graph where we plot at least 2 points to show the relationship between the dependent and independent variables. Watch and we'll show you.

Type: Tutorial

Linear Equations:

Equations of the form y = mx describe lines in the Cartesian plane which pass through the origin. The fact that many functions are linear when viewed on a small scale, is important in branches of mathematics such as calculus.

Type: Tutorial

Slope-Intercept Form:

Linear equations of the form y=mx+b can describe any non-vertical line in the cartesian plane. The constant m determines the line's slope, and the constant b determines the y intercept and thus the line's vertical position.

Type: Tutorial

Unit/Lesson Sequence

Direct and Inverse Variation:

"Lesson 1 of two lessons teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil). Lesson 2 teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases." from Insights into Algebra 1 - Annenberg Foundation.

Type: Unit/Lesson Sequence

Virtual Manipulatives

Graph a Line Using Y-Intercept and Slope:

This tutorial will help you to graph a line using its slope and y-intercept, or to identify the slope and y-intercept from a linear equation written in slope-intercept form.

Type: Virtual Manipulative

Linear Equations:

This resource provides guided practice for writing and graphing linear functions.

Type: Virtual Manipulative

Graphing Lines:

This manipulative will help you to explore the world of lines. You can investigate the relationships between linear equations, slope, and graphs of lines.

Type: Virtual Manipulative

Slope Slider:

In this activity, students adjust slider bars which adjust the coefficients and constants of a linear function and examine how their changes affect the graph. The equation of the line can be in slope-intercept form or standard form. This activity allows students to explore linear equations, slopes, and y-intercepts and their visual representation on a graph. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Graphing Lines:

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Type: Virtual Manipulative

Equation Grapher:

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

Type: Virtual Manipulative

MFAS Formative Assessments

Explaining Linear Functions:

Students are asked to describe defining properties of linear functions.

Linear or Nonlinear?:

Students are asked to identify a function as either linear or nonlinear and to justify their decision.

Nonlinear Functions:

Students are asked to provide an example of a nonlinear function and explain why it is nonlinear.

What Am I?:

Students are asked to describe a linear function, its graph, and the meaning of its parameters.

Original Student Tutorials Mathematics - Grades 9-12

Summer of FUNctions:

Have some fun with FUNctions!  Learn how to identify linear and non-linear functions in this interactive tutorial.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Summer of FUNctions:

Have some fun with FUNctions!  Learn how to identify linear and non-linear functions in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorials

Recognizing Linear Functions:

In this video, you will determine if the situation is linear or non-linear by finding the rate of change between cooordinates. You will check your work by graphing the coordinates given.

Type: Tutorial

Slope-Intercept Form from a Table:

In this video, you will practice writing the slope-intercept form for a line, given a table of x and y values.

Type: Tutorial

Finding the x and y intercepts from an equation:

Students will learn how to find and graph the x and y intercepts from an equation written in standard form.

Type: Tutorial

Graphing x and y intercepts from an equation:

Students will learn how to find the x and y intercepts from an equation in standard form.

Type: Tutorial

Finding intercepts from a table:

This tutorial shows students how to find the y inercept from a table.

Type: Tutorial

Slope-Intercept Equation from Two Solutions:

Given two points on a line, you will find the slope and the y-intercept. You will then write the equation of the line in slope-intercept form.

Type: Tutorial

Graphing a linear equation using a table:

Students will learn how to graph a linear equation using a table. Students will not be required to graph from slope-intercept form, although they will convert the equation from standard form to slope-intercpet form before they create the table.

Type: Tutorial

Graph a line in slope-intercept form:

This tutprial shows how to graph a line in slope-intercept form.

Type: Tutorial

Dependent and independent variables exercise: graphing the equation:

It's helpful to represent an equation on a graph where we plot at least 2 points to show the relationship between the dependent and independent variables. Watch and we'll show you.

Type: Tutorial

Linear Equations:

Equations of the form y = mx describe lines in the Cartesian plane which pass through the origin. The fact that many functions are linear when viewed on a small scale, is important in branches of mathematics such as calculus.

Type: Tutorial

Slope-Intercept Form:

Linear equations of the form y=mx+b can describe any non-vertical line in the cartesian plane. The constant m determines the line's slope, and the constant b determines the y intercept and thus the line's vertical position.

Type: Tutorial

Virtual Manipulatives

Slope Slider:

In this activity, students adjust slider bars which adjust the coefficients and constants of a linear function and examine how their changes affect the graph. The equation of the line can be in slope-intercept form or standard form. This activity allows students to explore linear equations, slopes, and y-intercepts and their visual representation on a graph. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Graphing Lines:

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Type: Virtual Manipulative

Equation Grapher:

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

Virtual Manipulative

Graphing Lines:

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Type: Virtual Manipulative