Beginning Algebra, 11th Edition

Completing Ordered Pairs to Estimate the Number

of Twin Births

The annual number of twin births in the United States from 2001 through 2006 can

be closely approximated by the linear equation

Number of twin births Year

which relates x, the year, and y, the number of twin births in thousands. (Source:

Department of Health and Human Services.)

(a)Complete the table of values for the given linear equation.

y=3.049x-5979.0,

EXAMPLE 6

182 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

NOW TRY
EXERCISE 6
Use the linear equation in
Example 6to estimate the
number of twin births in

2004. Interpret the results.

y (Number of Twin

x ( Year) Births, in thousands)

2001

2003

2006

y (Number of Twin

x ( Year) Births, in thousands)

2001 122

2003 128

2006 137

To find ywhen ,we substitute into the equation.

Let

yL 122 Use a calculator.

y=3.049 120012 - 5979.0 x=2001.

x= 2001

This means that in 2001, there were about 122 thousand (or 122,000) twin births.

We substitute the years 2003 and 2006 in the same way to complete the table.

means “is

approximately equal to.”

L

Ordered Pairs

1 2006, 137 2

1 2003, 128 2

1 2001, 122 2

1 x, y 2

Here each year xis paired

with the number of twin

births y(in thousands).

(b)Graph the ordered pairs found in part (a).

The ordered pairs are graphed in FIGURE 6. This graph of ordered pairs of data is

called a scatter diagram.

NUMBER OF TWIN BIRTHS

Year

115

0

120

125

130

135

140

y

x

200120022003200420052006

Twin Births (in thousands)

FIGURE 6

Notice the axes labels and scales.

Each square represents 1 unit in the

horizontal direction and 5 units in

the vertical direction. Because the

numbers in the first ordered pair

are large, we show a break in the

axes near the origin.

A scatter diagram enables us to tell whether two quantities are related to each

other. In FIGURE 6, the plotted points could be connected to approximate a straight line,

so the variables x(year) and y(number of twin births) have a linear relationship. The

increase in the number of twin births is also reflected. NOW TRY

NOW TRY ANSWER

6. ; There were
   approximately 131 thousand
   (or 131,000) twin births in the
   U.S. in 2004.

yL 131

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