# 11.3 Graphing with intercepts

 Page 1 / 4
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: $3x+4y=-12$ 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 $\left(0,-5\right)$ on the $x\text{-axis}$ or $y\text{-axis?}$
If you missed this problem, review Use the Rectangular Coordinate System .
3. Which ordered pairs are solutions to the equation $2x-y=6?$
$\phantom{\rule{0.2em}{0ex}}\left(6,0\right)\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\left(0,-6\right)\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}\left(4,-2\right).$
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 $x\text{-axis}$ and the $y\text{-axis}$ is called an intercept of the line.

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

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 $\left(a,0\right)$ ; 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 $x\text{-intercept}$ is the point, $\left(a,0\right),$ where the graph crosses the $x\text{-axis}.$ The $x\text{-intercept}$ occurs when $\text{y}$ is zero.

The $y\text{-intercept}$ is the point, $\left(0,b\right),$ where the graph crosses the $y\text{-axis}.$

The $y\text{-intercept}$ occurs when $\text{x}$ is zero.

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

Find the $x\text{- and}\phantom{\rule{0.2em}{0ex}}y\text{-intercepts}$ of each line:

$\phantom{\rule{0.2em}{0ex}}x+2y=4$ $\phantom{\rule{0.2em}{0ex}}3x-y=6$ $\phantom{\rule{0.2em}{0ex}}x+y=-5$ ## 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).

Find the $x\text{-}$ and $y\text{-intercepts}$ of the graph: $x-y=2.$ x -intercept (2,0): y -intercept (0,−2)

Find the $x\text{-}$ and $y\text{-intercepts}$ of the graph: $2x+3y=6.$ x -intercept (3,0); y -intercept (0,2)

I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
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)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight? By Rhodes   By    By By Jordon Humphreys By Rhodes