1. Representing Linear Patterns
Section 1.5

2. A DVD buyers club charges a $20 membership fee
and $15 per DVD purchased. The table below
represents this situation.
Number of DVDs purchased d 1 2 3 4 5
Total cost ($) 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

3. This is called a linear equation.
Number of DVDs purchased d 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

4. Number of CDs purchased
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 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

5. 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 1 2 3 4 5
Total cost ($) c 21 31 41 51 61 71
+10

6. 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).

7. dependent independent On a graph,
the independent variable is on the ________________ axis
and dependent variable is on the _______________ axis.
horizontal
vertical
dependent
independent

8. time t Distance Rate Time
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

9. Linear Equation:
Time (hours) t 2 4 6 8 10
Distance (miles) d
560
1120
1680
2240
2800
3000
2700
2400
2100
1800
1500
1200
900
600
300 2 4 6 8 10

10. 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 person’s 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 person’s age - r = a
220
age
Since the ________ depends on the ______, then ______ is the independent variable.
You can choose values for _________.
rate
age
age

11. age (years) a
Maximum
heart rate r 10 20 25 30 40 50
210
200
195
190
180
170