WHAT YOU LL LEARN Finding rates of change from

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

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.

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.

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.

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.

Find the rate of change for data graphed on the line. The explain what the rate of change means in this situation. (thousand feet) Height 3 (0, 2. 5) 2 1 (40, 1. 5) 0 20 40 60 Time (seconds) Find two points on the graph. Use the points to find the slope, which is also the rate of change. vertical change slope = horizontal change = = 1. 5 – 2. 5 40 – 0 1 40 1 The rate of change is 40 , which means that the parachute descends 1000 ft every 40 seconds.

Why is the height the dependent variable? The height of the parachute depends on the time it has descended. 25 ft (thousand feet) How many feet does the parachute descend in a second? Height 3 (0, 2. 5) 2 1 (40, 1. 5) 0 20 40 60 Time (seconds)

# of days Rental Company 1 $60 2 $75 3 $90 4 $105 5 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. $120 Hraibe’s 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. = =

# of days 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? Hraibe’s Yes; between any two pair of values in the table, the rate of change is $15 per day.

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. 8 Graph Table y x 6 2 units 4 2 3 units x 0 2 4 6 8 3 3 3 y 0 3 6 9 1 3 5 7 3 units 2 2 units

8 Graph Table y x 6 2 units 4 2 3 units x 0 2 4 6 8 3 3 3 y 0 3 6 9 1 3 5 7 3 units 2 2 units 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.

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.

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

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

Is the relationship shown by the data in the table linear? x y 1 1 1 3 4 5 6 1 -2 -5 -8 -3 -3 -3 YES

Is the relationship shown by the data in the table linear? x y 2 2 4 6 8 0 1 4 9 1 3 5 NO

Is the relationship shown by the data in the table linear? x y 1 1 1 0 1 2 3 3 6 9 12 3 3 3 YES

Is the relationship shown by the data in the table linear? x y 2 2 2 -3 5 -1 8 112 317 3 4 5 NO

Is the relationship shown by the data in the table linear? x y 7 7 7 1 0 8 1 15 2 22 3 1 1 1 YES

Is the relationship shown by the data in the table linear? x y -4 -4 -4 9 -4 5 1 1 6 -3 11 5 5 5 YES

Is the relationship shown by the data in the table linear? x y 2 1 3 13 37 49 715 4 2 6 YES Rate of change is 2.

Practice what you learned: Workbook Page 79 1 -10 Page 80 1 -10