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Rate of Change and Slope

mherbert avatar
mherbert
15 diapositives · 245 Views · Jan 04, 2020

Learn how to evaluate function rules and find rates of change and slopes in algebraic expressions and graphs. Practice finding slopes and rates of change using different examples.

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Rate of Change and Slope
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  1. Rate of Change and Slope ALGEBRA 1 LESSON 6-1 (For help, go to Lessons 5-2 and 1-5.) Evaluate each function rule for x = –5. 1. y = x – 7 2.y = 7 – x 3.y = 2x + 5 4.y = – x + 3 Write in simplest form. 5.6.7. 8.9.10. 2 5 7 – 3 3 – 1 3 – 5 6 – 0 8 – (–4) 3 – 7 –1 – 2 0 – 5 –6 – (–4) –2 – 6 0 – 1 1 – 0 8-3

  2. Rate of Change and Slope ALGEBRA 1 LESSON 6-1 Solutions 1.y = x – 7 for x = –5: y = –5 – 7 = –12 2.y = 7 – x for x = –5: y = 7 – (–5) = 12 3.y = 2x + 5 for x = –5: y = 2(–5) + 5 = –10 + 5 = –5 4.y = – x + 3 for x = –5: y = – (–5) + 3 = 2 + 3 = 5 5. = = 2 6. = – = – 7. = – = –3 8. = = 9. = = 10. = – = –1 2 5 2 5 7 – 3 3 – 1 4 2 3 – 5 6 – 0 2 6 1 3 8 – (–4) 3 – 7 12 4 –1 – 2 0 – 5 –3 –5 3 5 –6 – (–4) –2 – 6 –2 –8 1 4 0 – 1 1 – 0 1 1 8-3

  3. For the data in the table, is the rate of change the same for each pair of consecutive mileage amounts? Fee for Miles Driven Miles Fee 100 $30 150 $42 200 $54 250 $66 Rate of Change and Slope ALGEBRA 1 LESSON 6-1 Find the rate of change for each pair of consecutive mileage amounts. 8-3

  4. change in costCost depends on the change in number of milesnumber of miles. rate of change = 42 – 3012 54 – 4212 66 – 5412 150–100 50 200–150 50 200–250 50 = = = Rate of Change and Slope ALGEBRA 1 LESSON 6-1 (continued) The rate of change for each pair of consecutive mileage amounts is $12 per 50 miles. The rate of change is the same for all the data. 8-3

  5. Below is a graph of the distance traveled by a motorcycle from its starting point. Find the rate of change. Explain what this rate of change means. Choose two points On the graph (0,0) and (400,20) Rate of Change and Slope ALGEBRA 1 LESSON 6-1 8-3

  6. vertical changechange in distance horizontalchangechange in time rate of change = 400 – 0 20 – 0 400 20 20 Use two points. = Divide the vertical change by the horizontal change. = Simplify. = Rate of Change and Slope ALGEBRA 1 LESSON 6-1 (continued) Using the points (0,0) and (400,20), find the rate of change. The rate of change is 20 m/s. The motorcycle is traveling 20 meters each second. 8-3

  7. a. rise run 4 – 1 0 – 2 slope = = 3 –2 3 2 = = – 3 2 The slope of the line is – . Rate of Change and Slope ALGEBRA 1 LESSON 6-1 Find the slope of each line. 8-3

  8. Find the slope of the line. b. rise run –1 – 1 –2 – (–2) slope = = –2 –1 = = 2 Rate of Change and Slope ALGEBRA 1 LESSON 6-1 (continued) The slope of the line is 2. 8-3

  9. Find the slope of each line through E(3, –2) and F(–2, –1). –1 – (–2) –2 – 3 = y2 – y1 x2 – x1 slope = Substitute (–2, –1) for (x2, y2) and (3, –2) for (x1, y1). Simplify. 1 –5 1 5 = = – 1 5 The slope of EF is – . Rate of Change and Slope ALGEBRA 1 LESSON 6-1 8-3

  10. Find the slope of each line. a. y2–y1 x2 – x1 slope = 2 – 2 1– (–4) Substitute (1, 2) for (x2, y2) and (–4, 2) for (x1, y1). Simplify. = 0 5 = = 0 Rate of Change and Slope ALGEBRA 1 LESSON 6-1 The slope of the horizontal line is 0. 8-3

  11. y2 – y1 x2 – x1 slope = Substitute (2, 1) for (x2, y2) and (2, –4) for (x1, y1). 1 – (–4) 2 – 2 = 5 0 = Simplify. Rate of Change and Slope ALGEBRA 1 LESSON 6-1 (continued) Find the slope of the line. b. Division by zero is undefined. The slope of the vertical line in undefined. 8-3

  12. 1. Find the rate of change for the data in the table. 2. Find the rate of change for the data in the graph. 3. Find the slope of the line. Tickets Cost 5 $75 6 $90 7 $105 8 $120 4. Find the slope of the line through (3, –2) and (–2, 5). Rate of Change and Slope ALGEBRA 1 LESSON 6-1 8-3

  13. 5. State whether the slope is zero or undefined. a. b. Rate of Change and Slope ALGEBRA 1 LESSON 6-1 8-3

  14. Tickets Cost 5 $75 6 $90 7 $105 8 $120 7 5 – Rate of Change and Slope ALGEBRA 1 LESSON 6-1 1. Find the rate of change for the data in the table. 2. Find the rate of change for the data in the graph. 3. Find the slope of the line. $15 per ticket 4 3 400 calories per hour 4. Find the slope of the line through (3, –2) and (–2, 5). 8-3

  15. 5. State whether the slope is zero or undefined. a. b. Rate of Change and Slope ALGEBRA 1 LESSON 6-1 undefined 0 8-3