Effects of changing slope or y-intercept
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- Marjory Osborne
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1 Teacher Notes Parts 1 and 2 of this lesson are to be done on the calculator. Part 3 uses the TI-Navigator System. Part 1: Calculator Investigation of changing the y-intercept of an equation In your calculators y= screen enter the equation y = 2x + 5 into y 1 Question: What is the y-intercept of this equation? 5 Question: If the y-intercept were decreased by 7, what would be the new y-intercept? -2 Write a new equation using the new y-intercept and the same slope as the equation above. y=2x-2 Enter this equation into y 2 on your calculator. Compare the graphs. The graph moved down 7 units. Question: If the original y-intercept were increased by 3, what would be the new y- intercept? 8 Write a new equation using the new y-intercept and same slope as the original equation. y=2x+8 Enter this equation into y 2 on your calculator. Compare the graphs. The graph moved up 3 units Analysis: What effect does changing the y-intercept of an equation have on the graph? Increasing a y-intercepts moves the graph up. Decreasing a y-intercept moves the graph down. Teacher Notes Page 1 of 5
2 Part 2: Calculator investigation of changing the slope of an equation In your calculators y= screen enter the equation y = 2x + 5 into y 1 Question: What is the slope of this equation? 2 Question: If the original slope were doubled, what would be the new slope? 4 y=4x+5 The graph became steeper. Question: If the original slope were tripled, what would be the new slope? 6 y=6x+5 The graph became steeper. More steep than doubling the slope. Question: If the original slope were halved, what would be the new slope? 1 y=x+5 They became less steep (flatter). Analysis: What effect does changing the slope have on the graph? When multiplying by a number greater than 1 the graph becomes steeper. When multiplying by a number between 0 and 1 the graph will become less steep (flatter) Teacher Notes Page 2 of 5
3 Part 3: Assessment Section Get into the Navigator application on your calculator. We will answer a few quick poll questions based on the knowledge you just discovered from the previous parts. Load the Changing y-intercept activity setting. Before starting the quick polls assign the following colors to the matching equations. Red: 2x +5 White: 2x+2 Green: 2x+1 Blue: 2x 1 Orange: 2x 4 Use this activity setting for questions 1-3. Send quick polls set for multiple choice A-D. Question 1: Which line would you get if you increased the y-intercept of the green line by 4? a. Blue line c. Orange line Question 2: Which line would you get if you decreased the y-intercept of the white line by 3? a. Blue line c. Orange line d. Green line Question 3: Which line has a y-intercept that has been decreased from the blue line? a. Red line b. Orange line Teacher Notes Page 3 of 5
4 Load the Changing slope activity setting. Before starting the quick polls assign the following colors to the matching equations. Red: x +3 White: -.5x+3 Green: 2x+3 Blue: -2x+3 Orange: -x+3 Purple:.5x+3 Use this activity setting for questions 4-6. Send quick polls set for multiple choice A-E. Question 4: Which line would you get if you doubled the slope of the red line? b. Blue line Question 5: Which line would you get if you halved the slope of the blue line? Question 6: Which line would you get if you multiplied the slope of the white line by 4? d. Blue line Teacher Notes Page 4 of 5
5 Load the Changing slope and y-intercept activity setting. Should be the equation y=2x-1. Use this activity setting for questions 7-9. Question 7: What would be the equation you increased the y- intercept by 2 and multiplied the slope by -2? a. y = 4x 3 b. y = 1 4x c. y = 2 + 4x d. y = -4x 2 Question 8: What would be the equation you decreased the y- intercept by 6 and multiplied the slope by.5? a. y =.5x + 5 b. y = -6 x c. y = -7 + x d. y = x + 6 Question 9: What effect does increasing the y-intercept by 2 and keeping the same x-intercept have on the slope of the line? a. The slope is doubled b. The slope is halved c. There is no change in the slope d. The slope changes from positive to negative Teacher Notes Page 5 of 5
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