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Lesson 1 MI/Vocab

Use rate of change to solve problems. Find the slope of a line. rate of change. slope. Lesson 1 MI/Vocab.

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Lesson 1 MI/Vocab

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  1. Use rate of change to solve problems. • Find the slope of a line. • rate of change • slope Lesson 1 MI/Vocab

  2. A.6 The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. (A)Develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations. (B) Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs.Also addresses TEKS A.3(B). Lesson 1 TEKS

  3. Find a Rate of Change DRIVING TIMEThe table shows how the distance traveled changes with the number of hours driven. Use the table to find the rate of change. Explain the meaning of the rate of change. Each time x increases by 2 hours, y increases by 76 miles. Lesson 1 Ex1

  4. Answer: The rate of change is This means the speed traveled is 38 miles per hour. Find a Rate of Change Lesson 1 Ex1

  5. A. rate of change is This means that it costs $0.05 per minute to use the cell phone. B. rate of change is This means that it costs $5 per minute to use the cell phone. C. rate of change is This means that it costs $0.50 per minute to use the cell phone. D. rate of change is This means that it costs $0.20 per minute to use the cell phone. CELL PHONE The table shows how the cost changes with the number of minutes used. Use the table to find the rate of change. Explain the meaning of the rate of change. • A • B • C • D Lesson 1 CYP1

  6. millions of passports years Find a Rate of Change A. TRAVELThe graph to the right shows the number of U.S. passports issued in 2000, 2002, and 2004. Find the rates of change for 2000-2002 and 2002-2004. Use the formula for slope. Lesson 1 Ex2

  7. Find a Rate of Change 2000-2002: Substitute. Simplify. Answer: The number of passports issued decreased by 0.3 million in a 2-year period for a rate of change of –150,000 per year. Lesson 1 Ex2

  8. Find a Rate of Change 2002-2004: Substitute. Simplify. Answer: Over this 2-year period, the number of U.S. passports issued increased by 1.9 million for a rate of change of 950,000 per year. Lesson 1 Ex2

  9. Find a Rate of Change B. Explain the meaning of the rate of change in each case. Answer: For 2000-2002, on average, 150,000 fewer passports were issued each year than the last. For 2002-2004, on average, 950,000 more passports were issued each year than the last. Lesson 1 Ex2

  10. Find a Rate of Change C. How are the different rates of change shown on the graph? Answer: The first rate of change is negative, and the line goes down on the graph; the second rate of change is positive, and the graph goes upward. Lesson 1 Ex2

  11. A. AirlinesThe graph shows the number of airplane departures in the United States in recent years. Find the rates of change for 1990-1995 and 1995-2000. • A • B • C • D A. 1,2000,000 per year; 900,000 per year B. 8,100,000 per year; 9,000,000 per year C. 5 per year; 5 per year D. 240,000 per year; 180,000 per year Lesson 1 CYP2

  12. B. Explain the meaning of the slope in each case. • A • B • C • D A.For 1990-1995, the number of airplane departures increased by about 240,000 flights each year. For 1995-2000, the number of airplane departures increased by about 180,000 flightseach year. B. The rate of change increased by the same amount for 1990-1995 and 1995-2000. C. The number airplane departures decreased by about 240,000 for 1990-1995 and 180,000 for 1995-2000. D. For 1990-1995 and 1995-2000 the number of airplane departures was the same. Lesson 1 CYP2

  13. C. How are the different rates of change shown on the graph? • A • B • C • D A. There is a greater vertical change for 1990-1995 than for 1995-2000. Therefore, the section of the graph for 1990-1995 has a steeper slope. B. They have different y-values. C. The vertical change for 1990-1995 is negative, and for 1995-2000 it is positive. D. There is no difference shown in the graph. Lesson 1 CYP2

  14. Lesson 1 Key Concept 1

  15. Answer: Positive Slope Find the slope of the line that passes through (–3, 2) and (5, 5). Let (–3, 2) = (x1, y1) and (5, 5) = (x2, y2). Substitute. Simplify. Lesson 1 Ex3

  16. A.3 B. C. D.–3 Find the slope of the line that passes through (4, 5) and (7, 6). • A • B • C • D Lesson 1 CYP3

  17. Negative Slope Find the slope of the line that passes through (–3, –4) and (–2, –8). Let (–3, –4) = (x1, y1) and (–2, –8) = (x2, y2). Substitute. Simplify. Answer: The slope is –4. Lesson 1 Ex4

  18. A.2 B.–2 C. D. Find the slope of the line that passes through (–3, –5) and (–2, –7). • A • B • C • D Lesson 1 CYP4

  19. Zero Slope Find the slope of the line that passes through (–3, 4) and (4, 4). Let (–3, 4) = (x1, y1) and (4, 4) = (x2, y2). Substitute. Simplify. Answer: The slope is 0. Lesson 1 Ex5

  20. Find the slope of the line that passes through (–3, –1) and (5, –1). • A • B • C • D A. undefined B. 8 C. 2 D. 0 Lesson 1 CYP5

  21. Undefined Slope Find the slope of the line that passes through (–2, –4) and (–2, 3). Let (–2, –4) = (x1, y1) and (–2, 3) = (x2, y2). Answer: Since division by zero is undefined, the slope is undefined. Lesson 1 Ex6

  22. Find the slope of the line that passes through (5, –1) and (5, –3). • A • B • C • D A. undefined B. 0 C. 4 D. 2 Lesson 1 CYP6

  23. Lesson 1 Key Concept 2

  24. Find the value of r so that the line through (6, 3) and (r, 2) has a slope of Find Coordinates Given Slope Slope formula Substitute. Subtract. Lesson 1 Ex7

  25. Find Coordinates Given Slope 2(–1) = 1(r – 6) Find the cross products. Simplify. –2 = r – 6 Add 6 to each side. –2 + 6 = r – 6 + 6 Answer: 4 = r Simplify. Lesson 1 Ex7

  26. Find the value of p so that the line through (p, 4) and (3, –1) has a slope of A.5 B. C.–5 D.11 • A • B • C • D Lesson 1 CYP7

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