Intermediate Algebra (11th edition)

NOW TRY

NOTE While two points, such as the two intercepts in FIGURE 6, are sufficient

to graph a straight line, it is a good idea to use a third point to guard against

errors.

OBJECTIVE 6 Recognize equations of horizontal and vertical lines and lines

passing through the origin.A line parallel to the x-axis will not have an x-intercept.

Similarly, a line parallel to the y-axis will not have a y-intercept. We graph these types

of lines in the next two examples.

Graphing a Horizontal Line

Graph

Writing as shows that any value of x, including gives

Thus, the y-intercept is Since yis always 2, there is no value of xcor-

responding to so the graph has no x-intercept. The graph is shown with a table

of ordered pairs in FIGURE 7. It is a horizontal line.

y= 0,

y=2. 1 0, 2 2.

y= 2 0 x+ 1 y= 2 x=0,

y= 2.

EXAMPLE 3

140 CHAPTER 3 Graphs, Linear Equations, and Functions

x

y

0

(0, 3)

(– , 0^34 )

(–2, –5)

x-intercept

y-intercept

4 x – y = –3

FIGURE 6

xy

0

03

• 
  

  2 - 5

  
  


• 
  

  (^34)
  Use a third
  point as a
  check.
  NOW TRY
  EXERCISE 2
  Find the x- and y-intercepts,
  and graph the equation.
  x- 2 y= 4
  NOW TRY ANSWERS

  
  

2. 
   

   x-intercept: ;
   y-intercept:

   
   


3. 
   

1 0, - 22

1 4, 0 2

x – 2y = 4

0

y

x

–2^4

x

y

0

(0, 2)

Horizontal

y = 2 line

FIGURE 7

xy

2

02

32

• 1

To graph y 2,

do notsimply

graph the point

0, 2. The graph

is a line.

1 2

=

NOW TRY

–2 y = –2

0

y

x

–2 2

NOW TRY
EXERCISE 3
Graph y=-2.

The intercepts of are the points and Verify by sub-

stitution that also satisfies the equation. We use these ordered pairs to draw

the graph in FIGURE 6.

1 - 2, - 52

A- 1 0, 3 2.

3

4 x- y=- 3 4 , 0B

NOTE The horizontal line y= 0 is the x-axis.