# Lesson Plan: Graphing Linear Functions

## Lesson Objectives

• Graph linear functions
• Identify key features of linear graphs
• Write equations in different forms
• Evaluate functions

## TEKS Standards

• A.3(C): Graph linear functions and identify key features
• A.3(E): Determine effects of transformations on linear functions
• A.2(B): Write linear equations in various forms
• A.2(C): Write linear equations from various representations
• A.12(B): Evaluate functions

## 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:

 Equation Slope y-intercept y = 2x + 4 2 4 y = 3x - 7 3 -7 y = -4x - 9 -4 -9

## Teach (20 minutes)

### Definitions

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:

https://www.desmos.com/calculator/w5spiazzqr

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

https://www.media4math.com/library/21416/asset-preview

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

https://www.media4math.com/library/42998/asset-preview

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

https://www.media4math.com/library/74306/asset-preview

2. Graphical Representation

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

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

3. Tabular Representation

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

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

4. Verbal Representation

"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.

## Quiz

1. Graph y = 2x - 3

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

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)

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).