Unit 34: Functions and Representations

Day 15 of 30

Constant rate of change in linear functions

6-8Mathematics

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Learning Objective

Students will explore constant rate of change in linear functions through guided practice and application.

Today's Lesson

In this lesson, we'll explore constant rate of change in linear functions. Mathematical thinking develops logical reasoning and problem-solving abilities.

In algebra, expressions have different parts: In 5x + 3, the coefficient is 5 (the number multiplying the variable), the variable is x (the unknown), and the constant is 3 (the number alone). Coefficients tell you "how many" of the variable. Constants stay the same regardless of the variable's value. Understanding these parts helps you manipulate expressions correctly. For example, in 4x² - 7x + 2, coefficients are 4 and -7, variable is x, and constant is 2.

As you work through today's material, pay attention to the examples and try to identify the patterns or strategies being used. This will help you apply these concepts to new problems.

Take notes on key points and make connections to what you've already learned in previous lessons.

Key Terms
Problem

A mathematical question requiring analysis and solution

Solution

The result obtained by solving a problem

Activities
Instructions
1. Review the example problems for constant rate of change in linear functions. 2. Identify the steps and strategies used. 3. Work through practice problems independently. 4. Compare solutions with a partner.
Materials Needed
  • Notebook
  • Calculator (if needed)
  • Graph paper
Practice Problems
1

If f(x) = 3x + 2, find f(4)

Hint: Substitute 4 for x.
2

Is the relation {(1,2), (2,3), (1,4)} a function?

Hint: Check if any x-value repeats with different y.
3

If f(x) = x² - 1, find f(-2)

Hint: Substitute -2 for x. Remember (-2)² = 4.

Teaching Tip

For advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply constant rate of change in linear functions to novel situations.

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