Lesson 15: The Slope of a Non Vertical Line
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- Sabina Powell
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1 Classwork Opening Exercise Example Graph A Graph B a. Which graph is steeper? b. Write directions that explain how to move from one point on the graph to the other for each of Graph A and Graph B. c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)? Date: 4/5/14 S.62
2 Pair 1: Graph A Graph B a. Which graph is steeper? b. Write directions that explain how to move from one point on the graph to the other for each of Graph A and Graph B. c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)? Date: 4/5/14 S.63
3 Pair 2: Graph A Graph B a. Which graph is steeper? b. Write directions that explain how to move from one point on the graph to the other for each of Graph A and Graph B. c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)? Date: 4/5/14 S.64
4 Pair 3: Graph A Graph B a. Which graph is steeper? b. Write directions that explain how to move from one point on the graph to the other for each of Graph A and Graph B. c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)? Date: 4/5/14 S.65
5 Pair 4: Graph A Graph B a. Which graph is steeper? b. Write directions that explain how to move from one point on the graph to the other for each of Graph A and Graph B. c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)? Date: 4/5/14 S.66
6 Exercises Use your transparency to find the slope of each line if needed. 1. What is the slope of this non vertical line? 2. What is the slope of this non vertical line? 3. Which of the lines in Exercises 1 and 2 is steeper? Compare the slopes of each of the lines. Is there a relationship between steepness and slope? Date: 4/5/14 S.67
7 4. What is the slope of this non vertical line? 5. What is the slope of this non vertical line? Date: 4/5/14 S.68
8 6. What is the slope of this non vertical line? Date: 4/5/14 S.69
9 Lesson Summary Slope is a number that describes the steepness of a line. Slope is represented by the symbol. Lines that are left to right inclining have a positive slope, as shown below. Lines that are left to right declining have a negative slope, as shown below. Determine the slope of a line when the horizontal distance between points is fixed at 1 by translating point to the origin of the graph, and then identifying the coordinate of point. The slope of the line shown below is 2, so 2, because point is at 2 on the axis. Date: 4/5/14 S.70
10 Problem Set 1. Does the graph of the line shown below have a positive or negative slope? Explain. 2. Does the graph of the line shown below have a positive or negative slope? Explain. 3. What is the slope of this non vertical line? Use your transparency if needed. Date: 4/5/14 S.71
11 4. What is the slope of this non vertical line? Use your transparency if needed. 5. What is the slope of this non vertical line? Use your transparency if needed. Date: 4/5/14 S.72
12 6. What is the slope of this non vertical line? Use your transparency if needed. 7. What is the slope of this non vertical line? Use your transparency if needed. Date: 4/5/14 S.73
13 8. What is the slope of this non vertical line? Use your transparency if needed. 9. What is the slope of this non vertical line? Use your transparency if needed. Date: 4/5/14 S.74
14 10. What is the slope of this non vertical line? Use your transparency if needed. 11. What is the slope of this non vertical line? Use your transparency if needed. Date: 4/5/14 S.75
15 12. What is the slope of this non vertical line? Use your transparency if needed. 13. What is the slope of this non vertical line? Use your transparency if needed. Date: 4/5/14 S.76
16 14. What is the slope of this non vertical line? Use your transparency if needed. Date: 4/5/14 S.77
17 In Lesson 11, you did the work below involving constant rate problems. Use the table and the graphs provided to answer the questions that follow. 15. Suppose the volume of water that comes out in three minutes is 10.5 gallons. (time in minutes) Linear equation:. (in gallons) a. How many gallons of water flow out of the faucet per minute, that is, what is the unit rate of water flow? b. Assume that the graph of the situation is a line, as shown in the graph. What is the slope of the line? Date: 4/5/14 S.78
18 16. Emily paints at a constant rate. She can paint 32 square feet in five minutes. (time in minutes) Linear equation: (area painted in square feet).... a. How many square feet can Emily paint in one minute; that is, what is her unit rate of painting? b. Assume that the graph of the situation is a line, as shown in the graph. What is the slope of the line? Date: 4/5/14 S.79
19 17. A copy machine makes copies at a constant rate. The machine can make 80 copies in minutes. (time in minutes) Linear equation: (number of copies) a. How many copies can the machine make each minute; that is, what is the unit rate of the copy machine? b. Assume that the graph of the situation is a line, as shown in the graph. What is the slope of the line? Date: 4/5/14 S.80
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