Lesson Plan: Graphing Linear Functions 

Lesson Objectives

  • Graph linear functions using various methods
  • Interpret the meaning of slope and y-intercept from a graph
  • Identify the x-intercept and y-intercept of a linear function

Common Core Standards

  • F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

Prerequisite Skills

  • Understanding linear functions and equations
  • Plotting points on the Cartesian coordinate plane

Key Vocabulary

  • x-intercept
  • y-intercept
  • slope-intercept form
  • point-slope form
  • increasing function
  • decreasing function
  • standard form

Warm-up Activity (5 minutes)

Display three linear equations in slope-intercept form:

y = 2x + 4

y = 3x - 7

y = -4x - 9

Ask students to identify the slope and y-intercept for each equation. Have them complete a table like this:

y = 2x + 424
y = 3x - 73-7
y = -4x - 9-4-9


Teach (20 minutes)


Review the following video definitions:

Show these videos to explain increasing and decreasing functions. The videos describe these properties in the context of any function, but anchor the discussion to linear functions.

Use multiple representations to teach graphing linear functions:

1. Algebraic Representation

Show these equivalent linear equations but written in these forms:

  • Slope-intercept form: y = -x +1
  • Standard form: x + y = 1
  • Point-slope form: y-1 = (-x - 0)

Use this Desmos activity to explore these equivalent forms and explore others:


 Review this real-world application to generate an equation in standard form:


 Review how to convert from standard form to slope-intercept form:


 Finally review a step-by-step procedure for the point-slope form:


 2. Graphical Representation

Use this slide show to demonstrate graphing linear functions in slope-intercept form:


 3. Tabular Representation

Use this slide show to demonstrate multiple representations of linear functions that includes algebraic, graphical, and tabular:


 4. Verbal Representation

Start with a verbal representation that should be familiar to students:

"There is a linear relationship between the circumference of a circle and its radius. What is the linear function?"

Write the equation: C = k•d.

Ask students what k represents. For those who need help have them find the formula for the circumference of a circle.

Select one of these real-world applications of linear functions and show how to derive the appropriate equation:

5. Contextual Representation

Introduce this video, which is an application of linear functions in the context of excercise:


Review (15 minutes)

Have students review the different linear forms using these drag-and-drop activities:

Assess (10 minutes)

Administer a 10-question quiz to assess understanding.


  1. Graph y = 2x - 3
    Coordinate Grid
  2. Find the x- and y-intercepts of 3x - 2y = 6
  3. Write the equation of the line passing through (2, 5) with a slope of -1/2
  4. Graph 2x + 3y = 12
    Coordinate Grid
  5. Identify the slope and y-intercept of y = -4x + 7
  6. Find the slope of the line passing through (-1, 3) and (4, -2)
  7. Graph y - 1 = 2(x - 2)
    Coordinate Grid
  8. Write the equation of the line with y-intercept 5 and x-intercept -3
  9. Determine if y = -2x + 1 represents an increasing or decreasing function
  10. A company charges a $15 setup fee plus $8 per hour for their service. Write an equation representing the cost (y) in terms of hours (x).

Answer Key

  1. Coordinate Graph
  2. x-intercept: (2, 0), y-intercept: (0, -3)
  3. y - 5 = -1/2(x - 2) or y = -1/2x + 6
  4. Coordinate Graph
  5. Slope: -4, y-intercept: 7
  6. Slope = -1
  7. Coordinate Graph
  8. y = -5/3x + 5
  9. Decreasing function
  10. y = 8x + 15


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