About This Chapter
Standard: 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.
About This Chapter
Students who have gained proficiency in this standard are able to decide whether functions are linear, in addition to determining if they are increasing, decreasing, negative or positive. They can also find and apply the slopes and intercepts of lines.
Lessons in this standard cover concepts such as:
- Understanding the differences between nonlinear and linear functions
- Strategies for finding and applying the slopes of lines
- Tips for locating and using the intercepts of lines
Students demonstrate mastery of this standard when they can identify the traits of functions. They are also able to use the slope formula and the slope-intercept form to work with the slopes of lines. Mastery of this standard supports their college and career readiness because being able to interpret linear functions indicates preparedness for working with upper tier math concepts and helps students exercise their higher level thinking skills.
How to Use These Lessons in Your Classroom
Here are some tips for using these lessons to support instruction in the CCSS.Math.Content.8.F.A.3 standard:
Comparing and Identifying Functions Lessons
View the video lesson pertaining to the identification traits of functions. Discuss. Divide the class into six sections, each assigned to linear, nonlinear, increasing, decreasing, positive or negative. Within their groups, students will design an introduction 'speech' telling about their assigned identifying traits.
Finding and Applying the Slope of a Line Lessons
Challenge your students to complete the quiz before viewing this video. Share the lesson with your class. Upon completion, review the practice sections for using points and equations. Divide students into small groups, assigning practice exercises to each. After checking for accuracy, ask one student from each group to teach their problem with solution to the class.
Finding and Applying the Intercepts of a Line Lessons
Review x- and y-intercepts and the practice problems after viewing the video lesson. Ask students to write down on a slip of paper what they find to be the most challenging aspect of this lesson. After reflection, address those issues in a future class discussion to meet the students' learning needs.
1. How to Find and Apply The Slope of a Line
In this lesson, we'll discover all about the slopes of lines. We'll learn about different types of slopes and how to find the slopes of lines. We'll use two methods: the slope formula and the slope-intercept form.
2. How to Find and Apply the Intercepts of a Line
How can you take an equation of a line and find out where it will cross the x- or y-axis? In this lesson, we'll define x-intercepts and y-intercepts and learn how to find them.
3. How to Recognize Linear Functions vs Non-Linear Functions
In this lesson, you'll learn about two different groups of functions: linear and nonlinear. We'll cover how they look on a graph, and how you can tell them apart when they're written as equations.
4. Linear and Nonlinear Functions
After watching this video lesson, you'll be able to tell the differences between linear and nonlinear functions. You'll also be able to identify both types just by looking at graphs.
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Other chapters within the Common Core Math Grade 8 - Functions: Standards course