Lesson 6.1 Linear Equations & Functions

# Linear Equations

#### Materials

• CCB Mathematics pages 166 - 175

#### Standards

• Understand the connections between proportional relationships, lines, and linear equations.

• Analyze and solve linear equations and pairs of simultaneous linear equations.

#### Objectives

• Plot a line that represents the linear relationship between two sets of numbers

• Graphically determine the value of the dependent variable

• Determine whether an independent and a dependent variable are linearly related

• Write the equation of a line from a verbal description

#### Key Concept

• A variable is something you are trying to measure. There are two kinds of variables, independent and dependent. An independent variable has a value that remains the same. That is, it is not affected by a dependent variable. A dependent variable is a value that depends on other factors.

#### Vocabulary

Tier 2 Dependent VariableIndependent VariableRiseRunSlope Linear RelationshipY-Intercept Linear Equation

## Before Lesson

In this lesson, students learn to identify linear relationships. To determine student readiness, draw or project a coordinate grid on the board. Assign coordinate pairs to volunteers, and have them go to the board to plot them on the grid. Use students’ responses to determine if intervention is required.

## Background

Ask students to visualize an arcade filled with pinball machines. Each quarter that players put into a machine gives them three minutes of playing time. The amount of time never changes, but the number of quarters that players put in the machines does. Explain that the value that never changes is the independent variable, and the value that does is the dependent variable. Ask students to identify the variables in the example.

## Guided Practice

• Linear Relationships
• Complete a Data Table
• Linear Equations

## Core Skill

Solve Real-World Arithmetic Problems: Before reading the text as a class, explain that mathematical concepts, including linear relationships, are applied to many real-world situations. Read this section as a class and help students understand the data in the data table. Invite a volunteer to answer the problem.

Solve Linear Equations: Explain to students that the problem in the main section of the page works hand-in-hand with the sidebar activity. Read the problem for students. Then direct attention to the Core Skill sidebar.

You may want to pair students of different abilities to work through the steps outlined in the activity to calculate the slope of the suspension springs.

## Extension

Restate Definitions: Have students look at the graph at the top of page 171 again. Have them underline the words rise and run. Invite students to share what they know about these words and to model the words in pictures or actions. Then ask students to explain the meaning of each word in the context of the graph.

Investigate a Multi-Step Problem that Involves Planning and Reasoning: Since this lesson contains examples of linear relationships whose slopes are positive, have students investigate, describe, and solve real-world linear relationships for which the slope is negative, so that students appreciate their relevance. Share the example of how the elevation.