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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.
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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.
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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.
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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.
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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.
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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
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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
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# 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.
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# 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.
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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
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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
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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.
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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.
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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
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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
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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
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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
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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
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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
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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
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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.
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