# 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:

https://www.media4math.com/library/slideshow/applications-linear-equations

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)

### Definitions

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:

### Examples

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

https://www.media4math.com/library/slideshow/graphs-linear-functions

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

https://www.media4math.com/library/slideshow/math-examples-slope-intercept-form

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

https://www.media4math.com/library/40088/asset-preview

Here is a worksheet to accompany this activity:

https://www.media4math.com/library/40089/asset-preview

## Review (5 minutes)

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

https://www.media4math.com/library/4829/asset-preview

## Assess (10 minutes)

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

## Quiz

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.
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.

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