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
- 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