Page At what elevation did the skier start? Label the point on the graph representing your answer with the letter B. Point A represents that after 20 seconds, the skier is at an elevation of 220 feet. The skier started at an elevation of 320 feet. Point B should be labeled at (0, 320). 3. Why do you think the graph extends beyond the y-axis? The graph extends beyond the y-axis because the skier did not start at the very top of the hill, or because the graph represents only part of the skier’s trip.

4. About how many seconds would it take for the skier to reach the bottom of the hill? Explain your reasoning. The skier would reach the bottom of the hill in 64 seconds. I extended the line to where the elevation was How many feet did the skier descend down the hill each second? Explain your reasoning. The skier descends 5 feet each second. I divided the elevation at which the skier started (320 feet) by the number of seconds it would take to reach the bottom (64 seconds). 6. Label (24, 200) with C. How could you use points A and C to calculate the number of feet the skier descended each second? Point A is at (20, 220). Point C is at (24, 200). The difference in feet between the points is 20 feet. The difference in seconds between the points is 4 seconds. So, if the skier descended 20 feet in 4 seconds, then he or she descended 5 feet per second.

7. Write a rate to compare the change in elevation to the change in time at point A. Describe what the rate means. Make sure to state whether the rate is a rate of increase or a rate of decrease. 8. Write a rate to compare the change in elevation to the change in time at point C. Describe what the rate means. Make sure to state whether the rate is a rate of increase or a rate of decrease.

10. What do you notice about these unit rates? Explain your observation. The unit rates are the same. Because the graph is a straight line, the rate at which the skier descends is the same at every point. 11. What are the independent and dependent variables in the graph? The independent variable is the time in seconds. The dependent variable is the elevation of the skier in feet. 9. Write the rates of change at points A and C as unit rates.

12. What is the domain of the problem situation? Include units in your response. The domain is 0 seconds to 64 seconds What is the range of the problem situation? Include units in your response. The range is 320 feet to 0 feet. 14. What is the unit rate of change modeled in the graph? Use numerical values and units. State whether it is a rate of increase or a rate of decrease. The unit rate of change is 5 feet per second. It is a rate of decrease.

Before a skier started down a hill, he or she was at an elevation of 320 feet. The skier descended 5 feet every second. In 64 seconds, the skier reached an elevation of 0 feet, or the bottom of the hill.

16. Why is the rise the value for the numerator and the run the value for the denominator? The rise is the value of the numerator because it is the dependent variable, and the run is the value of the denominator because it is the independent variable. 17. What does it mean if a rate of change is negative? This means that it is a rate of decrease.

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Page 515 a. Restate the rate of change as a unit rate. Explain its meaning. Show your work. b. Why do you think Shelley did not read the unit rate of change from the graph? Shelley did not start with the unit rate because she would have had to estimate from the graph. She used coordinates with which she did not have to estimate values.

3. Restate the rate of change as a unit rate. Explain its meaning.

4. What is the cost of 10 items? Show your work. 5. Do you prefer to use the original rate of change determined from the graph, or the unit rate when making calculations? Explain your reasoning. Answers will vary. I prefer the unit rate. With the unit rate, it is easy to see whether my answer makes sense. I prefer the original rate. I can use the original rate to set up any proportion without converting it to a unit rate first.

Warm Up Graph the following equations. y = 4x - 3 y = -2x +1 y = 3 x = 4

Rate of change slope

Page 518 c. The two graphs look exactly alike. How could they show different rates of change? (0, 20) (60, 28) (6, 14) (0, 10)

(4, 18) (8, 12)(6, 12) (10, 6)

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