Lesson Plan: Introduction to Linear Functions 

Lesson Objectives

  • Define linear functions and their characteristics
  • Identify linear functions from equations and graphs
  • Understand the concept of slope and its relationship to linear functions

Common Core Standards

  • F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

Prerequisite Skills

  • Basic algebraic operations
  • Plotting points on the Cartesian coordinate plane

Key Vocabulary

  • Linear function
  • Slope
  • Y-intercept
  • Constant rate of change

Warm-up Activity (10 minutes)

Introduce the concept of linear functions by showing real-life examples. Use this slide show:


Or, use one of these these slide shows, which show a more detailed explanation of these real-world applications of linear functions.

Teach (25 minutes)


Define linear functions as relationships where the rate of change between variables is constant. Review these definitions:

 If necessary, review the definition of slope with this video definition:


Use this slide show to review the properties of linear functions before showing examples of graphs of linear functions:


Use this slide show to demonstrate examples of graphs of linear functions given the slope and y-intercept:


Use this Desmos activity to explore graphs of linear functions in slope-intercept form:


 Here is a worksheet to accompany this activity:


Review (5 minutes)

Use this drag-and-drop activity to review linear functions in slope-intercept form. Match the equation to the description:


Assess (10 minutes)

Administer a 10-question quiz to assess understanding of linear functions, slope, and graphing.


  1. Which equation represents a linear function?
    a) y = 2x + 3 
    b) y = x² 
    c) y = 3ˣ 
    d) y = 1/x
  2. What is the slope of the line y = -4x + 7?
  3. Identify the y-intercept of the function f(x) = 3x - 5.
  4. Graph the linear function y = 2x - 1.
    Coordinate Grid
  5. Is the function y = √x linear? Explain why or why not.
  6. Find the slope of the line passing through points (2, 5) and (4, 9).
  7. Write the equation of a line with slope 3 and y-intercept -2.
  8. Determine if the following table represents a linear function:
    x | 1 | 2 | 3 | 4
    y | 3 | 5 | 7 | 9
  9. What is the slope of a horizontal line?
  10. Sketch a graph of a linear function with a negative slope and positive y-intercept.
    Coordinate Grid

Answer Key

  1. a
  2. -4
  3. -5
  4. Coordinate Grid
  5. No, because it is not in slope-intercept or standard form.
  6. 2
  7. y = 3x - 2
  8. Yes, the rate of change is constant (2)
  9. 0
  10. Check that student graph shows a downward sloping line crossing the positive y-axis. Here is an example:
    Coordinate Graph


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