1. WHAT YOU’LL LEARN: Finding rates of change from tables and graphs. AND WHY: To find rates of change in real- world situations, such as the rate of descent for a parachute or the cost of renting a computer.

2. Suppose you type 140 words in 4 minutes. What is your typing rate? The number of words depends on the number of minutes you type. So, the number of words is the dependent variable.

3. Write each as a rate. a.You buy 5 yards of fabric for $19.95. b.You travel 268.8 mi on 12 gal of gasoline.

4. You use a rate of change to find the amount of one quantity per one unit of another, such as typing 35 words in 1 min. The RATE OF CHANGE allows you to see the relationship between two quantities that are changing.

5. On a graph, you show the dependent variable on the vertical axis and the independent variable on the horizontal axis. The SLOPE of a line is the RATE OF CHANGE relating the variables.

6. Find the rate of change for data graphed on the line. The explain what the rate of change means in this situation. (0,2.5) (40,1.5) Height (thousand feet) Time (seconds) 0 20 40 60 321321 Find two points on the graph. Use the points to find the slope, which is also the rate of change. = 40 – 0 1.5 – 2.5 horizontal change vertical change slope = = 40 1 The rate of change is, which means that the parachute descends 1000 ft every 40 seconds. 40 1

7. Why is the height the dependent variable? (0,2.5) (40,1.5) Height (thousand feet) Time (seconds) 0 20 40 60 321321 The height of the parachute depends on the time it has descended. How many feet does the parachute descend in a second? 25 ft

8. # of days Hraibe’s Rental Company 1$60 2$75 3$90 4$105 5$120 You can rent a computer from Hraibe’s Rental Company. The first day’s rent is $60. Find the rate of change for renting a computer after the first day. Rate of change == === The rate of change is 15/1, which means that it costs $15 for each day a computer is rented after the first day.

9. # of days Hraibe’s Rental Company 1$60 2$75 3$90 4$105 5$120 Will the rate of change for the data in the table be the same for any pair of data items? Yes; between any two pair of values in the table, the rate of change is $15 per day.

10. x y 0 1 3 6 5 9 7 The graph of a LINEAR FUNCTION is a line. You can also use a table to tell whether a relationship between sets of data is linear. 0 2 4 6 8 x y 86428642 2 units 3 units Graph Table 232323 2 units 3 units

11. As you can see from the table for the graph, the rate of change between consecutive pairs of data is constant. So, the relationship between the x-values and the y-values is linear. x y 0 1 3 6 5 9 7 0 2 4 6 8 x y 86428642 2 units 3 units Graph Table 23 23 23 2 units 3 units

12. Find the rate of change for each situation. 1.A baby is 18 in. long at birth and 27 in. at ten months. 2.The cost of group tickets for a museum is $48 for four people and $78 for ten people. 3.You drive 30 mi in one hour and 120 mi in four hours.

13. Find the rate of change for each situation. Cost (dollars) Weight (ounces) 0 1 2 3 4 5 6 2121 Find the rate of change. $1 buys 4 oz of oregano.

14. Find the rate of change for each situation. Find the rate of change. About 1 gal used for every 15 mi. Fuel in Tank (gallons) Miles Traveled 0 100 200 300 15 10 5

15. Find the rate of change for each situation. Is the relationship shown by the data in the table linear? YES x y 3 1 4 -2 5 -5 6 -8 -31 1 1

16. Find the rate of change for each situation. Is the relationship shown by the data in the table linear? NO x y 2 0 4 1 6 4 8 9 123252

17. Find the rate of change for each situation. Is the relationship shown by the data in the table linear? YES x y 0 3 1 6 2 9 3 12 313131

18. Find the rate of change for each situation. Is the relationship shown by the data in the table linear? NO x y -3 5 -1 8 112 317 324252

19. Find the rate of change for each situation. Is the relationship shown by the data in the table linear? YES x y 1 0 8 1 15 2 22 3 171717

20. Find the rate of change for each situation. Is the relationship shown by the data in the table linear? YES x y 9 -4 5 1 1 6 -3 11 5-45 5

21. Find the rate of change for each situation. Is the relationship shown by the data in the table linear? YES x y 1 3 3 7 4 9 715 422163 Rate of change is 2.