Linear Functions: Stations Activity

Objectives: 1. To graph linear equations. 2. To complete a table of values for each equation. 3. To identify the slope of linear equations in slope-intercept form. 4. To identify the y-intercept of linear equations in slope-intercept form. 5. To explain the effects of “m” on a linear function in slope-intercept form. 6. To explain the effects of “b” on a linear function in slope-intercept form.

Vocabulary: + linear function: a function used to create a line + parent function: the most basic form of a function, before adding constants + slope: the amount that the function increases or decreases as the x-value changes; the “m” value in an equation in slope-intercept form + y-intercept: the point on a graph where the line crosses the y-axis + slope-intercept form: linear equation in the form y = mx + b + x-axis: the horizontal axis + y-axis: the vertical axis

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 1 Station 1 y = mx

Equation A: y = x Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____)

Equation B:y = 2x Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 2 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How does the m value (the number in front of the x) change the way the graph looks? Write your answer in complete sentences.

Equation C: y = .5x

Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How does the m value (the number in front of the x) change the way the graph looks? Write your answer in complete sentences.

Equation D: y = 4x Fill in the table of values:

x y -2 -1 0 1 2

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 3 Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How does the m value (the number in front of the x) change the way the graph looks? Write your answer in complete sentences.

Equation E: y = .25x Fill in the table of values:

x Y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How does the m value (the number in front of the x) change the way the graph looks? Write your answer in complete sentences.

Station 1 “Big Idea” Questions: 1. Looking at the graphs you just created, what conclusions can you draw about rate of change for each equation? We define rate of change in a linear function as the slope of the function. Write your answer in a complete sentence.

2. If you are just looking at the equation, where do you look to find the slope?

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 4 a. Write your answer in a complete sentence:

b. Show an example using an equation you make up. (Circle or underline the slope):

3. Situation: William is part of a fundraiser at school. He earns $.50 for every candy bar he sells. Which graph represents the amount of money he earns? (Write the equation of the graph)

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 5 Station 2: y = -mx

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____)

Equation B: y = -x Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 6 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation C: y = -2x Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation D: y = -.5x Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided.

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 7 Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation E: y = -4x Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____ 2. How can you see this change in the equation? ______3. What is the y-intercept? (_____, _____) 4. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Station 2 “Big Idea” Questions: 1. What does the sign ( – or +) of the slope tell us about the line we are graphing? Write your answer in complete sentences.

2. Situation: Jacqui has money invested in the stock market. Unfortunately, the value of the stock has been decreasing at the rate of $2 per day. Which graph represents the amount of money Jacqui is losing?(Write the equation of the graph)

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 8 Station 3: y = x + b or y = x - b

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. What is the slope of the function? _____ 2. What is the y-intercept? (_____, _____)

Equation B: y = x + 1 Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. What is the slope of the function? _____

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 9 2. What is the y-intercept? (_____, _____) 3. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation C: y = x – 1 Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. What is the slope of the function? _____ 2. What is the y-intercept? (_____, _____) 3. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation D: y = x + 5 Fill in the table of values:

x y -2 -1 0 1 2

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 10 Plot the points on the grid provided. Answer the following questions: 1. What is the slope of the function? _____ 2. What is the y-intercept? (_____, _____) 3. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation E: y = x – 5 Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions: 1. What is the slope of the function? _____ 2. What is the y-intercept? (_____, _____) 3. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences Station 3 “Big Idea” Questions: 1. How does the b number change the way the graph looks? Write your answer in complete sentences.

2. How does the sign (+ or -) of the b number change the way the graph looks? Write your answer in complete sentences.

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 11 3. Situation: Christopher’s movie-rental plan charges $5 to set up, and then $1 for every movie rented. Which graph represents the amount of money he will pay using this plan? (Write the equation of the graph):

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 12 Station 4: y = mx + b or y = mx – b

Equation A:y = x Fill in the table of values:

x y -2 -1 0 1 2

Equation B: y = 2x + 1 Fill in the table of values:

x y -2 -1 0 1 2

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 13 3. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation C: y = -2x + 1 Fill in the table of values:

x y -2 -1 0 1 2

Equation D: y = 2x – 1 Fill in the table of values:

x y -2 -1 0 1 2

Plot the points on the grid provided. Answer the following questions:

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 14 1. What is the slope of the function? _____ 2. What is the y-intercept? (_____, _____) 3. How is this line different from the line of the parent function (y=x)? Write your answer in complete sentences.

Equation E: y = -2x - 1 Fill in the table of values:

x y -2 -1 0 1 2

Station 4 “Big Idea” Questions: 1. What does each part of the equation (in slope-intercept form) tell you about the line? Write your answer in complete sentences.

2. Situation: Danielle is short on cash. She starts off borrowing $1 from her mother on Monday. Unfortunately, she ends up borrowing $2 each day after that until payday. Which graph represents the amount of money Danielle will owe her mom when payday comes? (Write the equation of the graph)

E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 15