LEARN NC

K–12 teaching and learning · from the UNC School of Education

Walk the Line

This lesson demonstrates the effects of changing the slope and y-intercept on the graph and equation of a line.

A lesson plan for grades 8–12 Mathematics

By Carol Huss

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Learning outcomes

The student will learn how to write the equation of a line given its graph or its slope and y-intercept. The student will also learn the effects of changing the slope and y-intercept on the graph and the equation of the line.

Teacher planning

Time required for lesson

60.00 minutes

Materials/resources

*approximately 20 ft by 20 ft of floor space (floors with square tiles work best)
*wide masking tape (or laminated adding machine tape)
*magic marker
*graphing calculator

Technology resources

None

Pre-activities

The students should know the slope-intercept form of an equation and how to graph a line given its slope and y-intercept.

Activities

The teacher will select 2 students to place a 15-20 ft strip of masking tape (or laminated adding machine tape) on the floor. Then the teacher will select 2 students to place another 15-20 ft strip of tape on the floor perpendicular to the first strip. Use the tiles on the floor as graph paper. Next the teacher will ask students, one at a time, to take the magic marker and write on the tape the following:
1. x-axis
2. y-axis
3. 0 at the origin
4. scale the positive x-axis
5. scale the negative x-axis
6. scale the positive y-axis
7. scale the negative y-axis.

The teacher will choose a group of 5 students to stand at different points on the x-axis. Be sure one student stands on the origin. The teacher instructs the students to add 3 to the x-coordinate and move vertically to the result. For example, if Adam is standing on (-4, 0), he will move to (-4, -1) and if Beth is standing on (2, 0), she will move to (2, 5). The students will be points on a line. The teacher will ask the class “What is the equation of this line?” The answer is y = x + 3. The students return to their original starting point on the x-axis and the teacher chooses different values to add to x.

Next the teacher chooses another group of 5 students to stand on the x-axis and instructs them to subtract 3 from the x-coordinate. For example, Adam moves from (-4, 0) to (-4, -7) and Beth moves from (2, 0) to (2, -1). The teacher asks “What is the equation of this line?” (Answer: y = x - 3) Repeat several times, subtracting different values from x.

Then the teacher chooses another group of 5 students to stand on the x-axis and instructs them to multiply the x-coordinate by 2. “What is the equation of this line?” (Answer: y = 2x) Repeat using -2; (1/2); etc.

Lastly, the teacher will choose another group of 5 students to stand on the x-axis and instructs them to multiply the x-coordinate by 2 and subtract 1. “What is the equation of this line?” (Answer: y = 2x -1) Repeat several times using different combinations of positive/negative multipliers with adding/subtracting different values.

Assessment

The students will complete the following activities and questions.
MAY USE A GRAPHING CALCULATOR.
A. Write the equations of the lines in slope-intercept form. Then draw the graph of the lines, labeling each line with its equation. Answer the questions that follow.
1. slope = 1, y-intercept = 3
2. slope = 1, y-intercept = -3
3. slope = 1, y-intercept = 0
4. slope = 1, y-intercept = -1
How are these lines alike?
How are these lines different?
What was the effect of changing the y-intercept?
B. Write the equations of the lines in slope-intercept form. Then draw the graph of the lines, labeling each line with its equation. Answer the questions that follow.
1. slope = 1/2, y-intercept = 0
2. slope = 1, y-intercept = 0
3. slope = 3/2, y-intercept = 0
4. slope = 2, y-intercept = 0
How are these lines alike?
How are these lines different?
What was the effect of changing the slope?
C. Write the equations of the lines in slope-intercept form. Then draw the graph of the lines, labeling each line with its equation. Answer the questions that follow.
9. slope = 2, y-intercept = 3
10. slope = -2, y-intercept = 3
3. slope = 1/2, y-intercept = 3
4. slope = -1/2, y-intercept = 3
How are these lines alike?
How are these lines different?
What was the effect of changing the slope?

Also see the attachment: wtlwksht.rtf

Supplemental information

Attachment: wtlwksht.rtf

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North Carolina Curriculum Alignment

Mathematics (2004)

Grade 8

  • Goal 5: Algebra - The learner will understand and use linear relations and functions.
    • Objective 5.01: Develop an understanding of function.
      • Translate among verbal, tabular, graphic, and algebraic representations of functions.
      • Identify relations and functions as linear or nonlinear.
      • Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
      • Interpret and compare properties of linear functions from tables, graphs, or equations.
    • Objective 5.02: Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.

Grades 9–12 — Introductory Mathematics

  • Goal 4: Algebra - The learner will understand and use linear relations and functions.
    • Objective 4.01: Develop an understanding of function.
      • Translate among verbal, tabular, graphic, and algebraic representations of functions.
      • Identify relations and functions as linear or nonlinear.
      • Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
      • Interpret and compare properties of linear functions from tables, graphs, or equations.
    • Objective 4.02: Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.