# This means that Rodrigo earns by HC120730133036

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```									Lesson 4-4

Example 1 Identify Linear Relationships
PART-TIME JOB The amount of money Rodrigo                   Number of       Amount
earns is shown for different numbers of hours                Hours          Earned
worked. Is the relationship between the amount                  5             \$70
earned and the hours worked linear? If so, find the            10            \$140
constant rate of change. If not, explain your                  15            \$210
reasoning.                                                     20            \$280

Examine the change in the number of hours worked and in the amount earned.

Number of      Amount
Hours         Earned
5            \$70
+5        10           \$140         +70         As the number of hours increases by
+5        15           \$210         +70         5, the amount earned increases by
70.
+5        20           \$280         +70

Since the rate of change is constant, this is a linear relationship. The constant rate of
70
change is      or \$14 per hour. This means that Rodrigo earns \$14 for every hour that he
5
works.
y
2500
Example 2 Find a Constant Rate of Change                     2250
RECREATION Find the constant                                 2000

Water (gallons)
rate of change for the amount of                             1750
water in the swimming pool each                              1500
hour as it is being filled. Interpret                        1250
its meaning.                                                 1000

750

500
Choose any two points on the line and
250
find the rate of change between them.
1   2   3   4   5   6   7   8   x

(2, 500)  2 hours, 500 gallons                                                     Hours
(5, 1,250)  5 hours, 1,250 gallons

change in gallons (1,250  500 ) gallons
                                The amount of water changed from 500 to
change in time        (5  2) hours              1,250 gallons between hours 2 and 5.
750 gallons
                                 Subtract to find the change in gallons and
3 hours                       the change in time.

250 gallons
                                  Express this rate as a unit rate.
1 hour

The amount of water added to the swimming pool each hour is 250 gallons.
Example 3 Identify Proportional Relationships
CAR RENTAL Use the graph to determine if there is a proportional linear
relationship between the number of days a car is rented and the total charge.
y
200

180

160
Charge (\$)

140

120

100

80

60

40

20

1     2   3     4     5    6    7     8    x

Days

Since the graph of the data forms a line, the relationship between the two scales is linear.
This can also be seen in the table of values created using the points on the graph.

+20   +20       +20   +20       +20     Constant Rate of Change
Charge (\$)                  40     60    80       100   120       140      change in charge 20

Days                         1      2     3        4     5         6        change in days    1
+1    +1        +1    +1        +1

To determine if the two scales are proportional, express the relationship between the
charges for several days as a ratio.

charge                      40              100             140
                        40              25             23.33
days                       1                4               6

Since the ratios are not all the same, the total charge is not proportional to the number of
days a car is rented.

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