Lesson Plan: Graphing Linear Functions

Lesson Objectives

Graph linear functions using different methods
Understand slope-intercept form
Interpret slope and y-intercept in real-world contexts

Florida BEST Standards

MA.912.F.1.1: Classify functions as linear, quadratic, cubic, exponential, logarithmic, rational, or absolute value.
MA.912.F.1.2: Determine key features of function graphs including extrema, end behavior, intercepts, domain, and range.
MA.912.AR.2.3: Write linear two-variable equations from various representations.
MA.912.AR.2.4: Graph linear functions and determine key features.
MA.912.AR.2.5: Solve and graph problems modeled with linear functions.
MA.912.F.2.1: Identify effects of transformations on function graphs.

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:

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).