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)