# 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.

- Cricket chirps vs. Temperature:
__https://www.media4math.com/library/slideshow/application-linear-functions-cricket-chirps__ - Cost vs. time for renting equipment:
__https://www.media4math.com/library/slideshow/application-linear-functions-cost-vs-time__ - Distance vs. time:
__https://www.media4math.com/library/slideshow/application-linear-functions-distance-vs-time__

## Teach (25 minutes)

### Definitions

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

- Linear Function:
__https://www.media4math.com/library/22087/asset-preview__ - Slope-intercept Form:
__https://www.media4math.com/library/42988/asset-preview__ - Rate of Change:
__https://www.media4math.com/library/42989/asset-preview__ - y-intercept:
__https://www.media4math.com/library/42996/asset-preview__

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

- Which equation represents a linear function?

a) y = 2x + 3

b) y = x²

c) y = 3ˣ

d) y = 1/x - What is the slope of the line y = -4x + 7?
- Identify the y-intercept of the function f(x) = 3x - 5.
- Graph the linear function y = 2x - 1.
- Is the function y = √x linear? Explain why or why not.
- Find the slope of the line passing through points (2, 5) and (4, 9).
- Write the equation of a line with slope 3 and y-intercept -2.
- Determine if the following table represents a linear function:

x | 1 | 2 | 3 | 4

y | 3 | 5 | 7 | 9 - What is the slope of a horizontal line?
- Sketch a graph of a linear function with a negative slope and positive y-intercept.

## Answer Key

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

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