<p>Linear Functions: Stations Activity</p><p>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.</p><p>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</p><p>E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 1 Station 1 y = mx</p><p>Equation A: y = x Fill in the table of values:</p><p> x y -2 -1 0 1 2</p><p>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? (_____, _____)</p><p>Equation B:y = 2x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____</p><p>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.</p><p>Equation C: y = .5x</p><p>Fill in the table of values:</p><p> x y -2 -1 0 1 2</p><p>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.</p><p>Equation D: y = 4x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>Equation E: y = .25x Fill in the table of values: </p><p> x Y -2 -1 0 1 2</p><p>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.</p><p>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.</p><p>2. If you are just looking at the equation, where do you look to find the slope? </p><p>E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 4 a. Write your answer in a complete sentence: </p><p> b. Show an example using an equation you make up. (Circle or underline the slope):</p><p>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)</p><p>E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 5 Station 2: y = -mx</p><p>Equation A: y = x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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? (_____, _____)</p><p>Equation B: y = -x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>Plot the points on the grid provided. Answer the following questions: 1. How do the y values change each time x increases by 1? _____</p><p>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.</p><p>Equation C: y = -2x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>Equation D: y = -.5x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>Plot the points on the grid provided.</p><p>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.</p><p>Equation E: y = -4x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>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.</p><p>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)</p><p>E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 8 Station 3: y = x + b or y = x - b</p><p>Equation A: y = x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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? (_____, _____)</p><p>Equation B: y = x + 1 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>Plot the points on the grid provided. Answer the following questions: 1. What is the slope of the function? _____</p><p>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.</p><p>Equation C: y = x – 1 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>Equation D: y = x + 5 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>Equation E: y = x – 5 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>2. How does the sign (+ or -) of the b number change the way the graph looks? Write your answer in complete sentences.</p><p>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):</p><p>E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 12 Station 4: y = mx + b or y = mx – b</p><p>Equation A:y = x Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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? (_____, _____)</p><p>Equation B: y = 2x + 1 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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? (_____, _____)</p><p>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.</p><p>Equation C: y = -2x + 1 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>Equation D: y = 2x – 1 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>Plot the points on the grid provided. Answer the following questions:</p><p>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.</p><p>Equation E: y = -2x - 1 Fill in the table of values: </p><p> x y -2 -1 0 1 2</p><p>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.</p><p>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.</p><p>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)</p><p>E. Fischer (with T. Hassell, E. Lossia, F. Scott) pg. 15</p>