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https://www.cpalms.org/PreviewStandard/Preview/5500
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.
Standard #: MAFS.8.F.1.3Archived Standard
Standard Information
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
Content Complexity Rating:
Level 2: Basic Application of Skills & Concepts
-
More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
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Related Resources
Formative Assessments
- 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 areĀ asked to describe defining properties of linear functions.
Lesson Plans
-
Beginning Linear Functions This lesson is designed to introduce students to the concept of slope. 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
- 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
- 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
- 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.
Professional Development
- Direct and Inverse Variation This professional development video shows the teaching of direct and indirect proportions, and the related concepts of the slopes, equations, y-intercepts, etc. Comments about the use of correct terminology and other best practices are included.
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.
- 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.
MFAS Formative Assessments
- Explaining Linear Functions Students areĀ 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 6-8
- 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.
- 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 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.
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.