K-12 Teaching and Learning From the UNC School of Education

Learn more

Related pages

  • Investigating linear equations: Using a graphic calculator to compare the slope and y-intercept of lines to understand the slope-intercept form (y = mx+b) and what effect each has on a line.
  • To be or not to be... linear: The student will determine the correlation between two variables. They will graph ordered pairs on a coordinate plane, determine a best fit line, find slope and intercepts, and write the equation of a line. This lesson plan is geared for both 8th grade math and algebra.
  • Pilots and flight engineers: Working with slope-intercept form: In this lesson, students compete in relay races to complete a series of problems involving slope-intercept form. Students discuss the importance of mathematical reasoning and teamwork in aviation careers.

Related topics

Help

Please read our disclaimer for lesson plans.

Legal

The text of this page is copyright ©2008. See terms of use. Images and other media may be licensed separately; see captions for more information and read the fine print.

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 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
  • handout

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

  1. 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.
  2. 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
  3. 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.
  4. 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.
  5. 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.
  6. 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. Students may use a graphing calculator. (Note: the problems and questions below are identical to those on the handout.)

  1. 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?
  2. 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?
  3. 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 = 2, y-intercept = 3
    • 2. 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?

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 8

        • Functions
          • 8.F.3Interpret 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...
          • 8.F.4Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph....
      • High School: Algebra

        • Creating Equations
          • ALG.CE.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
      • High School: Functions

        • Interpreting Functions
          • FUN.IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph square root,...
        • Linear, Quadratic, & Exponential Models
          • FUN.LQE.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

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.

Grade 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.