Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

The line graph in FIGURE 1presents information based on a


method for locating a point in a plane developed by René


Descartes, a 17th-century French mathematician. Legend has it


that Descartes, who was lying in bed ill, was watching a fly crawl


about on the ceiling near a corner of the room. It occurred to him


that the location of the fly could be described by determining its


distances from the two adjacent walls. See the figure.


We use this insight to plot points and graph linear equations in two variables


whose graphs are straight lines.


OBJECTIVE 2 Plot ordered pairs. Each of the pairs of numbers


and


is an example of an ordered pair—that is, a pair of numbers written within paren-


theses, consisting of a first componentand a second component.We graph an


ordered pair by using two perpendicular number lines that intersect at their 0 points,


as shown in the plane in FIGURE 2. The common 0 point is called the origin.


1 3, 2 2 , 1 - 5, 6 2 , 1 4, - 12


136 CHAPTER 3 Graphs, Linear Equations, and Functions


OBJECTIVES OBJECTIVE 1 Interpret a line graph.The line graph in FIGURE 1shows per-


sonal spending (in billions of dollars) on medical care in the United States from 2000


through 2007. About how much was spent on medical care in 2006? (We will answer


this question shortly.)


The Rectangular Coordinate System


3.1


1 Interpret a line
graph.
2 Plot ordered pairs.
3 Find ordered pairs
that satisfy a given
equation.
4 Graph lines.
5 Find x- and
y-intercepts.
6 Recognize equations
of horizontal and
vertical lines and
lines passing
through the origin.
7 Use the midpoint
formula.

Locating a fly
on a ceiling

FIGURE 1

2000 2002 2004 2006

Spending (in billions

of dollars)

Source: U.S. Department of Commerce.

Personal Spending on Medical Care

Year

1000

1100

1200

1400
1300

1500

1600

1700

1800

1900

x

y

0

Origin y-axis

x-axis

Rectangular coordinate system
FIGURE 2

René Descartes (1596–1650)
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