*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

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

## Problem-Solving Task

## Student Center Activity

## Tutorials

## Unit/Lesson Sequence

## Virtual Manipulatives

## MFAS Formative Assessments

Students are asked to describe defining properties of linear functions.

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

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

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

## Original Student Tutorials Mathematics - Grades 9-12

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

## Student Resources

## Original Student Tutorial

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

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

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

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

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

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

Type: Tutorial

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

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

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

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

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

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

## Problem-Solving Task

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

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