Representing Linear Patterns

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Representing Linear Patterns
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• A DVD buyers club charges a 20 membership fee
• and 15 per DVD purchased. The table below
• represents this situation.

Number of DVDs purchased d 0 1 2 3 4 5
Total cost () c 20 35 50 65 80 95
15
15
15
15
15
Find the first differences for the total cost.
constant
linear
Since the data shows a ___________ difference the
pattern is __________. If a pattern is linear
then its graph is a straight _________.
line
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Number of DVDs purchased d 0 1 2 3 4 5
Total cost () c 20 35 50 65 80 95

• The equation represents
  this situation.
• This is called a linear equation.

80
70
Constant difference or price per DVD
Membership fee
60
50
40
30
20
10
1
2
3
4
5
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• Example 1 The costs associated with being a
  member of a
• CD Club are presented in the table below.
• Find the first differences and write an equation
  to represent the
• data pattern.

Number of CDs purchased n 0 1 2 3 4 5
Total cost () c 26 39 52 65 78 91
13
13
13
13
13
13
The club charges _________ per CD. The cost for
0 CDs is ____________. Therefore, the club
membership (initial cost) must be _________.
26
26
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• Try this
• The table shows the costs associated with being a
  
• member of a DVD club that charges a membership
• fee. Write an equation to represent the pattern
  in
• the data.

Number of DVDs purchased n 0 1 2 3 4 5
Total cost () c 21 31 41 51 61 71
10
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• Remember from Example 1
• n represented the number of CDs purchased and
• c represented the total cost

Linear equations contain an independent variable
and a dependent variable.
independent
dependent
In this case n is called the ________________
variable and c is called the ____________________
____ variable.
The total cost (c) depends on the number of CD
purchased (n).
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• On a graph,
• the independent variable is on the
  ________________ axis
• and dependent variable is on the _______________
  axis.

horizontal
vertical
dependent
independent
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• Example 2
• A jet airplane is flying at a rate of 280 miles
  per hour.

Write a linear equation to express the distance
traveled in a given amount of time. Graph the
equation for times from 0 to 10 hours.
The distance traveled can be represented by
__________________ ________________ x
_______________
Distance
Rate
Time
To find the ordered pairs (points) for the graph,
make a table. Since distance depends on time,
________________ is the independent variable,
and you can choose values for ___.
time
t
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Time (hours) t 0 2 4 6 8 10
Distance (miles) d
Linear Equation
0
560
1120
1680
2240
2800
3000
2700
2400
2100
1800
1500
1200
900
600
300
4
2
8
6
10
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• Example 3 Exercise physiologists suggest that a
  reasonable estimate for the maximum heart rate
  during exercise is no more than 220 beats per
  minute minus the persons age. Represent the
  maximum heart rate by r and the age by a. Write
  a linear equation to express the maximum heart
  rate (r) , in terms of age (a). Create a table
  for ages from 10 to 50.

Rate equals 220 beats minus the persons age
-
r

a
220
age
Since the ________ depends on the ______, then
______ is the independent variable. You can
choose values for _________.
rate
age
age
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age (years) a
Maximum heart rate r
10
20
25
30
40
50
210
200
195
190
180
170