Beginning Algebra, 11th Edition

Graphing an Equation of the Form (Vertical Line)

Graph

First we add 3 to each side of the

equation to get All

ordered-pair solutions of this equation

have x-coordinate 3. Any number can be

used for y. We show three ordered pairs

that satisfy the equation in the table of

values. The graph is the vertical line

shown in FIGURE 14. The x-intercept is

1 3, 0 2. There is no y-intercept.

x- 3 = 0 x= 3.

x- 3 = 0.

EXAMPLE 6 xk

192 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

xy

33

30

32 -

Line through the Origin

If Aand Bare nonzero real numbers, the graph of a linear equation of the form

passes through the origin 1 0, 0 2.

AxBy 0

OBJECTIVE 4 Graph linear equations of the form or .Con-

sider the following linear equations:

which can be written ;

which can be written

When the coefficient of xor yis 0, the graph of the linear equation is a horizontal or

vertical line.

x= 3, x+ 0 y= 3.

y=-4, 0 x+ y=- 4

yk xk

NOW TRY
EXERCISE 5
Graph .y= 2

Graphing an Equation of the Form (Horizontal Line)

Graph

For any value of x, yis always equal

to 4. Three ordered pairs that satisfy

the equation are shown in the table of

values. Drawing a line through these

points gives the horizontal lineshown

in FIGURE 13. The y-intercept is.

There is no x-intercept.

1 0, - 42

-

y=-4.

EXAMPLE 5 yk

y = –4

(0, – 4)

y-intercept

Horizontal line

x

y

–2

2

–2

04

–4

2

(–2, – 4) (3, – 4)

–4

4

FIGURE 13

x – 3 = 0

x-intercept (3, 0)

Vertical

line

x

y

–2

2

–2

04

–4

2

(3, 3)

(3, –2)

–4

4

FIGURE 14

NOW TRY
EXERCISE 6
Graph .x+ 4 = 0

xy

24

04

34 -

• 
  


• 
  
  
  
  • 
    
  
  
  
  

NOW TRY

Horizontal Line

The graph of the linear equation where kis a real number, is the horizon-

tal line with y-intercept. There is no x-intercept (unless the horizontal line

is the x-axis itself ).

1 0, k 2

yk,

xcan be any

real number.

ymust be - 4.

ycan be any

real number.

xmust be 3.

NOW TRY

NOW TRY ANSWERS
5.

6. 
   

x

y

0

2 y = 2

x

y

–4 0

x + 4 = 0

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