Standard #: MAFS.8.F.1.3 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



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: 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 - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :

    Function notation may not be used.

    Calculator :

    Yes

    Context :

    Allowable



Sample Test Items (4)

Test Item # Question Difficulty Type
Sample Item 1

Several functions represent different savings account plans.

Which functions are nonlinear?

N/A MS: Multiselect
Sample Item 2 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.

N/A OR: Open Response
Sample Item 3

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

What is true about the function?

N/A MC: Multiple Choice
Sample Item 4

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?

N/A SHT: Selectable Hot Text


Related Courses

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1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))


Related Resources

Formative Assessments

Name Description
What Am I?

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

Nonlinear Functions

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

Linear or Nonlinear?

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

Explaining Linear Functions

Students are asked to describe defining properties of linear functions.

Lesson Plans

Name Description
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.
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.

Original Student Tutorials

Name Description
Summer of FUNctions

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

Scatterplots Part 6: Using Linear Models

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 5: Interpreting the Equation of the Trend Line

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

This is part 5 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 4: Equation of the Trend Line

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Perspectives Video: Professional/Enthusiast

Name Description
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.

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Task

Name Description
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.

Student Center Activity

Name Description
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.

Tutorials

Name Description
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.

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.

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.

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.

Finding intercepts from a table

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

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.

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.

Graph a line in slope-intercept form

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

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.

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.

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.

Unit/Lesson Sequence

Name Description
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.

Virtual Manipulatives

Name Description
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.

Linear Equations

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

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.

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.

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.

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).

Student Resources

Original Student Tutorials

Name Description
Summer of FUNctions:

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

Scatterplots Part 6: Using Linear Models :

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 5: Interpreting the Equation of the Trend Line :

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

This is part 5 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Problem-Solving Task

Name Description
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.

Student Center Activity

Name Description
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.

Tutorials

Name Description
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.

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.

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.

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.

Finding intercepts from a table:

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

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.

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.

Graph a line in slope-intercept form:

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

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.

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.

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.

Virtual Manipulatives

Name Description
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.

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.

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).



Parent Resources

Problem-Solving Task

Name Description
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.

Virtual Manipulative

Name Description
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.



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