Beginning Algebra, 11th Edition

SECTION 3.2 Graphing Linear Equations in Two Variables^189

This gives the ordered pairs and To find a third point, we let

Let

Multiply.

y= 6 Add.

y= 3 + 3

y=- x=- 2.

3

2

1 - 22 + 3

y=-

3

2

x+ 3

1 0, 3 2 1 2, 0 2. x=-2.

NOW TRY

EXERCISE 1

Graph. 2 x- 4 y= 8 The ordered pairs are and. We find a third ordered pair (as a check)

by choosing some other number for xor y. We choose.

Let

Multiply.

Add 10.

,or Divide by 4. Write in lowest terms.

This gives the ordered pair or We plot the three ordered pairs

, and A 7 and draw a line through them, as shown in FIGURE 9.

1

1 5, 0 2 2 , 2B,

A^152 , 2B, A^7 12 , 2B.^1 0, -^42 ,

15

2

x=

30

4

4 x= 30

4 x- 10 = 20

4 x- 5122 = 20 y=2.

4 x- 5 y= 20

y= 2

10 , - 42 15 , 02

Write each x-value first.

( , 2)

(^712)
(^712)
4 x – 5 y 20
y
0
5

• 4
  0
  2

x

• 110357
  
  
  • 4
    
    
    • 2
    
    
    
    
  
  
  
  

2

x

y

(0, –4)

(5, 0)

FIGURE 9 NOW TRY

Graphing a Linear Equation

Graph

Although this linear equation is not in standard form it could

be written in that form. To find two different points on the graph, we first let

and then let.

Let. Let

Multiply. Add

y = 3 Add. x= 2 Multiply by 32.

3

2 x.

3

2

y= 0 + 3 x= 3

0 =- y= 0.

3

2

y=- x= 0 x+ 3

3

2

102 + 3

y=-

3

2

y=- x+ 3

3

2

x+ 3

y= 0

x= 0

1 Ax+ By=C 2 ,

y=- 32 x+3.

EXAMPLE 2

NOW TRY ANSWER

1. 
   

x

y

0

(0, –2)

(4, 0)

2 x – 4y = 8

Choosing a multiple of

2 makes multiplying

by easier.-^32

All three points should lie on

the same straight line. If

they don’t, double-check

the ordered pairs.