Linear Functions (Guided Lesson)

​Linear Functions

By Dana Wake

Let's Start This Lesson With a Warm-up! (It will count as a grade.)

Multiple Choice

Which of these statements is the best definition of a function?

• A set of ordered pairs.

• A set of ordered pairs such that each input has exactly one output.

• A set of ordered pairs such that each output has exactly one input.

Math Response

What is the function notation?

Do not write any words. WRITE THE FUNCTION NOTATION ONLY. NO SPACES.

Type answer here

Correct Answer: f\left(x\right)

Deg^°

Rad

Multiple Choice

What is the domain of the function below?

$$\left\{\left(1,9\right),\ \left(-2,4\right),\ \left(-8,2\right),\ \left(-1,3\right)\right\}$$

• $$\left\{1,-1,-2,-8\right\}$$

• $$\left\{9,4,2,3\right\}$$

• $$\left\{-2,\ 2,\ 3,\ 1\right\}$$

Drag and Drop

$$f\left(-2\right)=$$ ​

Placeholder

$$f\left(0\right)=$$ ​

Placeholder

$$f\left(4\right)=$$ ​

Placeholder

​

Drag these tiles and drop them in the correct blank above

1

0

-1

-2

-4

Multiple Choice

What is the range of $$f\left(x\right)=9-7x$$ if the given domain is $$\left\{-1,\ 3\right\}$$

• {16, -12}

• {2, -12}

• {16, 30}

• {2, 30}

Linear Functions

Definition

Linear Function

Definition

m and b

• m is the variable representation for slope

• b is the variable representation for the y-intercept

Let's discuss the y-intercept first! (Pay attention because you will be asked questions.)

Define the y-intercept

Definition

The y-intercept is the y-coordinate of the point where the graph of a relation intersects the y-axis.

Hotspot

Click on the y-intercept on the graph.

Define the y-intercept

The y-intercept can be written as a coordinate point! The y-intercept on this graph is (0, 4). Notice that for the y-intercept, the value of the x coordinate is 0. This will always be true!

Multiple Select

Which coordinate points represent y-intercept? Select ALL that apply.

• (0, -7)

• (-7, 0)

• (0, 5)

• (0, -13)

• (10, 0)

Multiple Choice

What is the y-intercept of the graph?

• (0, -2)

• (-2, 0)

• (0, -4)

• (-4, 0)

Now, let's discuss slope.

Multiple Choice

Which variable represents slope?

• m

• b

• x

• y

Definition of Slope

The slope of a line is a measure of its steepness and direction. A line that rises from left to right has positive slope. A line that falls from left to right has negative slope. Look at slope guy Bob!

Multiple Choice

What variable represents the y-intercept?

• m

• b

• x

• y

Labeling

Label each type slope on slope guy Bob!

Drag labels to their correct position on the image

Zero Slope

Undefined slope

Positive slope

Negative slope

Multiple Choice

What type of slope is shown in the graph?

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

What type of slope is shown on the graph?

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

What type of slope is shown in the graph?

• Positive

• Negative

• Undefined

• Zero

How Do You Find the Slope on a Graph?

Count!

Examine the Count - Finding Slope

rise

run

Hotspot

Choose the coordinates that are in the cross-points of the graph.

Linear Function

Now, that you know what the slope is

Replace this with your body text. Duplicate this text as many times as you would like. All provided templates can be reused multiple times. Wish you a good day.

Happy teaching!

Multiple Choice

Is the slope positive or negative?

• Positive

• Negative

Multiple Choice

What is the rise of the graph?

• -6

• 6

• 3

• -3

Multiple Choice

What is the run of the graph?

• -6

• 6

• 3

• -3

Multiple Choice

What is the slope?

$$m=\frac{rise}{run}$$

• $$m=-\frac{6}{3}=-2$$

• $$m=\frac{6}{3}=2$$

• $$m=-\frac{3}{6}=-\frac{1}{2}$$

• $$m=\frac{3}{6}=\frac{1}{2}$$

Labeling

Label each graph with the correct slope.

Drag labels to their correct position on the image

Complete the Slope Handout

Calculate the Slope Using the Slope Formula

1) Find two coordinate points on the graph.

2) Label each point as 1 or 2.

3) Substitute into the slope formula.

4) Calculate the slope.

Using the Slope Formula

• Coordinate point 1________________

• Coordinate point 2 _______________

• x₁ = _{__________________}

• x₂ = ______________

• y₁= ______________

• y₂= ______________

Complete the Calculating Slope Handout

Multiple Choice

What is the y-intercept of the graph?

• b = -4

• b = -2

• b = 2

• b = 4

Multiple Choice

What is the slope of the graph?

• m = -2

• m = 2

• m = 4

• m = -4

Creating a Linear Function from a Graph

Now, you understand how to find the slope, m, and the y-intercept, b.
This means that you know how to create a linear function from a graph.

Drag and Drop

What function is represented on the graph? Find m and find b, then substitute into the function.

$$f\left(x\right)=$$ ​ ​ ​ ​

Placeholder

$$x$$ +​

Placeholder

Drag these tiles and drop them in the correct blank above

2

-4

Match

Match each graph to the correct function.

• $$f\left(x\right)=-\frac{3}{4}x+2$$

• $$f\left(x\right)=-\frac{3}{4}x-2$$

• $$f\left(x\right)=\frac{3}{4}x-2$$

Graphing Linear Functions

To graph a linear function, you need a minimum of two points. More points the better but you only need two! Follow the steps below:

1) Plot the y-intercept first

2) Use the slope as a road map to find the second point

3) Use the slope to find another point

Practice graphing linear functions using the handout

Graphing

Graph the linear function $$f\left(x\right)=\frac{7}{3}x-4$$

Graphing

Graph the linear function $$f\left(x\right)=-\frac{2}{3}x+6$$

Exit Ticket Time!

Clear your desk. Put all notes away

This will count as an assessment grade.