WHAT YOU’LL LEARN: Finding rates of change from tables and graphs. AND WHY: To find rates of...
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![Page 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.](https://reader030.fdocuments.us/reader030/viewer/2022032605/56649e795503460f94b79bc8/html5/thumbnails/1.jpg)
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)
Heig
ht
(thousa
nd f
eet)
Time (seconds)0 20 40 60
3
2
1
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.
401
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Why is the height the dependent variable?
(0,2.5)
(40,1.5)H
eig
ht
(thousa
nd f
eet)
Time (seconds)0 20 40 60
3
2
1
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 13 36 59 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 8
6
4
2
2 units
3 units
GraphTable
23
23
23
2 units3 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 13 36 59 7
0 2 4 6 8
x
y 8
6
4
2
2 units
3 units
GraphTable
23
23
23
2 units3 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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Cost
(dolla
rs)
Weight (ounces)
0 1 2 3 4 5 6
2
1
Find the rate of change.
$1 buys 4 oz of oregano.
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Find the rate of change.
About 1 gal used for every 15 mi.
Fuel in
Tank
( gallo
ns)
Miles Traveled0 100 200 300
15
10
5
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Is the relationship shown by the data in the table linear?
YES
x y
3 14 -25 -56 -8
-31
-31
-31
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Is the relationship shown by the data in the table linear?
NO
x y
2 04 16 48 9
12
32
52
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Is the relationship shown by the data in the table linear?
YES
x y
0 31 62 93 12
31
31
31
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Is the relationship shown by the data in the table linear?
NO
x y
-3 5-1 8 112 317
32
42
52
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Is the relationship shown by the data in the table linear?
YES
x y
1 0 8 115 222 3
17
17
17
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Is the relationship shown by the data in the table linear?
YES
x y
9 -4 5 1 1 6-3 11
5-4
5-4
5-4
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Is the relationship shown by the data in the table linear?
YES
x y
1 33 74 9715
42
21
63
Rate of change is 2.