Beginning Algebra, 11th Edition

NOTE In a plane, bothnumbers in the ordered pair are needed to locate a point. The

ordered pair is a name for the point.

SECTION 3.1 Linear Equations in Two Variables; The Rectangular Coordinate System 181

NOW TRY
EXERCISE 5
Plot the given points in a co-
ordinate system.

, , ,

A^52 , 3B, ,^1 - 4, -^321 - 4, 0^2

1 - 3, 1 2 1 2, - 42 1 0, - 12

Right 2 Up 3

x

y

–6 –4 2 4 6

–2

–4

–6

2

4

6

–2 0

Positive (^2 ,^3 )

direction

Positive

direction

x-coordinate

y-coordinate

FIGURE 4

x

y

246

–2

–6

2

4

6

–6 –4 –2 0

(0, 0)

3

(–2, 3) (^2 , 2)

(5, 0)

(3, –2)

(–1, –4) (0, –3)

(4, –3.75)

Quadrant III Quadrant IV

Quadrant II Quadrant I

FIGURE 5

Plotting Ordered Pairs

Plot the given points in a coordinate system.

(a) (b) (c) (d) (e)

(f ) (g) (h) (i)

The point from part (a) is plotted(graphed) in FIGURE 4. The other points

are plotted in FIGURE 5.

In each case, begin at the origin. Move right or left the number of units that corre-

sponds to the x-coordinate in the ordered pair—right if the x-coordinate is positive or

left if it is negative.Then turn and move up or down the number of units that corre-

sponds to the y-coordinate —up if the y-coordinate is positive or down if it is negative.

1 2, 3 2

1 4, -3.75 2 1 5, 0 2 1 0, - 32 1 0, 0 2

a

3

2

1 2, 3 2 1 - 1, - 42 1 - 2, 3 2 1 3, - 22 , 2b

EXAMPLE 5

Notice the difference in the locations of the points and in

parts (c) and (d). The point is in quadrant II, whereas the point is in

quadrant IV. The order of the coordinates is important. The x-coordinate is always

given first in an ordered pair.

To plot the point in part (e), think of the improper fraction as the mixed

number and move or units to the right along the x-axis. Then turn and go

2 units up, parallel to the y-axis. The point in part (f ) is plotted similarly,

by approximating the location of the decimal y-coordinate.

In part (g), the point lies on the x-axis since the y-coordinate is 0. In part (h),

the point lies on the y-axis since the x-coordinate is 0. In part (i), the point

is at the origin. Points on the axes themselves are not in any quadrant.

NOW TRY

1 0, 0 2

1 0, - 32

1 5, 0 2

1 4, -3.75 2

(^1) B
1

A 2

3

(^12)
1
2
3

A 2

3

2 , 2B

1 - 2, 3 2 1 3, - 22

1 - 2, 3 2 1 3, - 22

Sometimes we can use a linear equation to mathematically describe, or model,a

real-life situation, as shown in the next example.

NOW TRY ANSWER
5.

x

y

0

(–3, 1)  , 3^52 

(0, –1)

(–4, –3)(2, –4)

(–4, 0)