# 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* = 2*x* + 4

*y* = 3*x* - 7

*y* = -4*x* - 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:

- Slope-intercept form:
__https://www.media4math.com/library/74604/asset-preview__ - Increasing function:
__https://www.media4math.com/library/74601/asset-preview__ - Decreasing function:
__https://www.media4math.com/library/74602/asset-preview__ - x-intercept:
__https://www.media4math.com/library/74609/asset-preview__ - y-intercept:
__https://www.media4math.com/library/74608/asset-preview__ - Point-slope form:
__https://www.media4math.com/library/74606/asset-preview__ - Standard form:

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.

- Increasing functions:
__https://www.media4math.com/library/44909/asset-preview__ - Decreasing functions:
__https://www.media4math.com/library/44910/asset-preview__

### 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**

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:

- 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__

**5. Contextual Representation**

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

__https://www.media4math.com/library/21299/asset-preview__

## Review (15 minutes)

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

- Slope-intercept:
__https://www.media4math.com/library/4829/asset-preview__ - Standard form:
__https://www.media4math.com/library/4830/asset-preview__ - Point-slope form:
__https://www.media4math.com/library/4841/asset-preview__

## Assess (10 minutes)

Administer a 10-question quiz to assess understanding.

## Quiz

- Graph y = 2x - 3

- Find the x- and y-intercepts of 3x - 2y = 6

- Write the equation of the line passing through (2, 5) with a slope of -1/2

- Graph 2x + 3y = 12

- Identify the slope and y-intercept of y = -4x + 7

- Find the slope of the line passing through (-1, 3) and (4, -2)

- Graph y - 1 = 2(x - 2)

- Write the equation of the line with y-intercept 5 and x-intercept -3

- Determine if y = -2x + 1 represents an increasing or decreasing function

- 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

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

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