<< Chapter < Page Chapter >> Page >
By the end of this section, you will be able to:
  • Identify the intercepts on a graph
  • Find the intercepts from an equation of a line
  • Graph a line using the intercepts
  • Choose the most convenient method to graph a line

Before you get started, take this readiness quiz.

  1. Solve: 3 x + 4 y = −12 for x when y = 0 .
    If you missed this problem, review Solve Equations using the Division and Multiplication Properties of Equality .
  2. Is the point ( 0 , −5 ) on the x -axis or y -axis?
    If you missed this problem, review Use the Rectangular Coordinate System .
  3. Which ordered pairs are solutions to the equation 2 x y = 6 ?
    ( 6 , 0 ) ( 0 , −6 ) ( 4 , −2 ) .
    If you missed this problem, review Use the Rectangular Coordinate System .

Identify the intercepts on a graph

Every linear equation    has a unique line that represents all the solutions of the equation. When graphing a line by plotting points, each person who graphs the line can choose any three points, so two people graphing the line might use different sets of points.

At first glance, their two lines might appear different since they would have different points labeled. But if all the work was done correctly, the lines will be exactly the same line. One way to recognize that they are indeed the same line is to focus on where the line crosses the axes. Each of these points is called an intercept of the line .

Intercepts of a line

Each of the points at which a line crosses the x -axis and the y -axis is called an intercept of the line.

Let’s look at the graph of the lines shown in [link] .

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through two labeled points, “ordered pair 0, 6” and ordered pair 3, 0”.

First, notice where each of these lines crosses the x - axis:

Figure: The line crosses the x-axis at: Ordered pair of this point
42 3 (3,0)
43 4 (4,0)
44 5 (5,0)
45 0 (0,0)

Do you see a pattern?

For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form ( a , 0 ) ; and is called the x-intercept of the line. The x- intercept occurs when y is zero.

Now, let's look at the points where these lines cross the y-axis.

Figure: The line crosses the y-axis at: Ordered pair for this point
42 6 (0,6)
43 -3 (0,-3)
44 -5 (0,-5)
45 0 (0,0)

x- Intercept and y- Intercept of a line

The x -intercept is the point, ( a , 0 ), where the graph crosses the x -axis . The x -intercept occurs when y is zero.

The y -intercept is the point, ( 0 , b ), where the graph crosses the y -axis .

The y -intercept occurs when x is zero.

  • The x-intercept occurs when y is zero.
  • The y-intercept occurs when x is zero.

Find the x - and y -intercepts of each line:

x + 2 y = 4

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 0, 2” and “ordered pair 4, 0”.

3 x y = 6

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 0, -6” and “ordered pair 2, 0”.

x + y = −5

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 0, -5” and “ordered pair -5, 0”.

Solution

The graph crosses the x -axis at the point (4, 0). The x -intercept is (4, 0).
The graph crosses the y -axis at the point (0, 2). The x -intercept is (0, 2).
The graph crosses the x -axis at the point (2, 0). The x -intercept is (2, 0)
The graph crosses the y -axis at the point (0, −6). The y -intercept is (0, −6).
The graph crosses the x -axis at the point (−5, 0). The x -intercept is (−5, 0).
The graph crosses the y -axis at the point (0, −5). The y -intercept is (0, −5).
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find the x - and y -intercepts of the graph: x y = 2 .

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 0, 2” and “ordered pair 2, 0”.

x -intercept (2,0): y -intercept (0,−2)

Got questions? Get instant answers now!

Find the x - and y -intercepts of the graph: 2 x + 3 y = 6 .

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 0, 2” and “ordered pair 3, 0”.

x -intercept (3,0); y -intercept (0,2)

Got questions? Get instant answers now!

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 1

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?

Ask