Introduction

Use the sliders in GeoGebra: Graphing Lines with the Same Slope to graph

  • y = 2x + 8
  • y = 2x − 4
  • y = 2x + 1
  • y = 2x − 7

To graph these lines in GeoGebra, you will need to do the following:

  1. Move the first slider so that the slope = 2.
  2. Change each of the following sliders to the correct y-intercept of each line.

Question #1 - Complete this sentence: Lines with equal slopes form a set of _____ (Fill in the blank) lines.

Now, use GeoGebra to graph:

  1. y = −3x + 8
  2. y equals one-third x minus 4

Now, graph

  1. y = 6x + 1
  2. y equals negative one-sixth x plus 1

Question #2 - How are the slopes related in each of the above pairs of equations?

Question #3 - What type of lines are formed in this situation? If you need more graphs to determine the answers to the above questions use these:

  • y equals negative one-half x
  • y + 2x + 3
  • y = −x − 5
  • y = x + 2

Now, answer these questions:

  1. Complete this sentence: Lines with equal slopes form a set of _________ (Fill in the blank) lines.
  2. How are the slopes related in each of the Graph Set 2 equations?
  3. What types of lines are formed in the Graph Set 2 equations?

Lesson Objectives

Following successful completion of this lesson, students will be able to...

  • Create equations in two or more variables to represent relationships between quantities.

Enduring Understandings

  • You can solve real-world problems using equations and inequalities.
  • Operations create relationships between numbers.
  • The language of mathematics is communicated through specialized vocabulary and symbols used to represent and describe mathematical ideas, generalizations, and relationships.
  • By describing patterns using mathematics, we can make predictions and generalizations, analyze situations in everyday life, and sort and classify things.

The above objectives correspond with the Alabama Course of Study: Algebra II with Statistics standards: 8, 13, and 16.