Representing Linear Patterns

Section 1.5

Since the data shows a ___________ difference the pattern is __________.

If a pattern is linear then its graph is a straight _________.

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

line

The equation represents this situation.

This is called a linear equation. 15 20c d

Number of DVDs purchased d 0 1 2 3 4 5

Total cost ($) c 20 35 50 65 80 95

Constant difference or price per DVD

Membership fee

1 2 3 4 5

20

10

30

40

50

80

70

60

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 thedata 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

The club charges _________ per CD. The cost for 0 CDs is ____________. Therefore, the club membership (initial cost) must be _________.

$13$26

$26

13 26c n

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

+1010 21c n

Remember from Example 1:

n represented the number of CDs purchased and

c represented the total cost

13 26c n

Linear equations contain an independent variable and a dependent variable.

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).

dependentindependent

On a graph,

the independent variable is on the ________________ axis

and dependent variable is on the _______________ axis.

independent

dependent

horizontal

vertical

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

280d t

4 2 8 6 10

300

600

900

1200

1500

1800

2100

2400

2700

3000

Time (hours) t 0 2 4 6 8 10

Distance (miles) d280d tLinear Equation:

0 560 1120 1680 2240 2800

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 = 220

Since the ________ depends on the ______, then ______ is the independent variable.

You can choose values for _________.

- a

rate age

age

age

220r a age (years) aMaximumheart rate

r

10 20 25 30 40 50

210 200 195 190 180 170