Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1
Completing Ordered Pairs and Making a Table

In parts (a) – (d), complete each ordered pair for Then, in part (e), write


the results as a table of ordered pairs.


2 x+ 3 y=6.


EXAMPLE 1


138 CHAPTER 3 Graphs, Linear Equations, and Functions


(a) 0,


Let
Multiply, and
then add.
Divide by 3.

The ordered pair is


(b) , 0


Let
Multiply, and
then add.
Divide by 2.

The ordered pair is 13 , 02.


x= 3


2 x= 6


2 x+ 3102 = 6 y=0.


2 x+ 3 y= 6


1 2


10 , 22.


y= 2


3 y= 6


2102 + 3 y= 6 x=0.


2 x+ 3 y= 6


1 2


(c)


Let
Multiply.
Add 6.
Divide by 3.

The ordered pair is.


(d) ,


Let
Multiply.
Add 12.
Divide by 2.

The ordered pair is 19 , - 42.


x= 9


2 x=^18


2 x- 12 = 6


2 x + 31 - 42 = 6 y=-4.


2 x+ 3 y= 6


1 - 42


1 - 3 , 42


y= 4


3 y= 12


- 6 + 3 y= 6


21 - 32 + 3 y= 6 x=-3.


2 x+ 3 y= 6


1 - 3, 2


(e) We write a table of these ordered pairs as shown.


Represents the ordered pair 0, 2 1 2

xy
0 2
3 0
3 4
9 - 4





OBJECTIVE 4 Graph lines. The graph of an equationis the set of points cor-


responding to allordered pairs that satisfy the equation. It gives a “picture” of the


equation.


To graph we plot the ordered pairs found in Objective 3and


Example 1.These points, plotted in FIGURE 4(a), appear to lie on a straight line. If all


the ordered pairs that satisfy the equation were graphed, they would


form the straight line shown in FIGURE 4(b).


2 x+ 3 y= 6


2 x+ 3 y= 6,


NOW TRY
EXERCISE 1
Complete the table of ordered
pairs for 2x-y=4.


xy
0
0
4
2

NOW TRY ANSWER



  1. xy
    0
    20
    44
    32

    • 4




y


  • 3
    0
    3
    6
    9


4
2
0


  • 2

  • 4


x


2468

2


  • 2

  • 4 – 2

  • 4


4

0
(6, –2)

(9, –4)


(–3, 4)


(0, 2)
(3, 0) x

y
y


  • 3
    0
    3
    6
    9


4
2
0


  • 2

  • 4


x


2468

2


  • 2

  • 4 – 2

  • 4


4

0
(6, –2)

(9, –4)


(–3, 4)


(0, 2)
(3, 0) x

y

2 x 3 y 6


(a) (b)
FIGURE 4

NOW TRY

Represents the ordered pair 3, 0
Represents the ordered pair 3, 4
Represents the ordered pair 9, 4 1 - 2

1 - 2

1 2
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