<< Chapter < Page Chapter >> Page >

Graph using the intercepts: y = 3 x .


The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12.  A line passes through the points “ordered pair 0, 0” and “ordered pair 1, 3”.

Got questions? Get instant answers now!

Graph using the intercepts: y = x .


The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12.  A line passes through the points “ordered pair 0, 0” and “ordered pair 1, -1”.

Got questions? Get instant answers now!

Choose the most convenient method to graph a line

While we could graph any linear equation    by plotting points, it may not always be the most convenient method. This table shows six of equations we’ve graphed in this chapter, and the methods we used to graph them.

Equation Method
#1 y = 2 x + 1 Plotting points
#2 y = 1 2 x + 3 Plotting points
#3 x = −7 Vertical line
#4 y = 4 Horizontal line
#5 2 x + y = 6 Intercepts
#6 4 x 3 y = 12 Intercepts

What is it about the form of equation that can help us choose the most convenient method to graph its line?

Notice that in equations #1 and #2, y is isolated on one side of the equation, and its coefficient is 1. We found points by substituting values for x on the right side of the equation and then simplifying to get the corresponding y- values.

Equations #3 and #4 each have just one variable. Remember, in this kind of equation the value of that one variable is constant; it does not depend on the value of the other variable. Equations of this form have graphs that are vertical or horizontal lines.

In equations #5 and #6, both x and y are on the same side of the equation. These two equations are of the form A x + B y = C . We substituted y = 0 and x = 0 to find the x- and y- intercepts, and then found a third point by choosing a value for x or y .

This leads to the following strategy for choosing the most convenient method to graph a line.

Choose the most convenient method to graph a line.

  1. If the equation has only one variable. It is a vertical or horizontal line.
    • x = a is a vertical line passing through the x -axis at a
    • y = b is a horizontal line passing through the y -axis at b .
  2. If y is isolated on one side of the equation. Graph by plotting points.
    • Choose any three values for x and then solve for the corresponding y - values.
  3. If the equation is of the form A x + B y = C , find the intercepts.
    • Find the x - and y - intercepts and then a third point.

Identify the most convenient method to graph each line:

  1. y = −3
  2. 4 x −6 y = 12
  3. x = 2
  4. y = 2 5 x −1

Solution

y = −3

This equation has only one variable, y . Its graph is a horizontal line crossing the y -axis at −3 .

4 x −6 y = 12

This equation is of the form A x + B y = C . Find the intercepts and one more point.

x = 2

There is only one variable, x . The graph is a vertical line crossing the x -axis at 2 .

y = 2 5 x −1

Since y is isolated on the left side of the equation, it will be easiest to graph this line by plotting three points.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Identify the most convenient method to graph each line:

  1. 3 x + 2 y = 12
  2. y = 4
  3. y = 1 5 x −4
  4. x = −7
  1. intercepts
  2. horizontal line
  3. plotting points
  4. vertical line
Got questions? Get instant answers now!

Identify the most convenient method to graph each line:

  1. x = 6
  2. y = 3 4 x + 1
  3. y = −8
  4. 4 x −3 y = −1

  1. vertical line
  2. plotting points
  3. horizontal line
  4. intercepts

Got questions? Get instant answers now!

Key concepts

  • Intercepts
    • 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 y is zero.
    • The x- intercept occurs when y is zero.
    • The y- intercept occurs when x is zero.
  • Find the x and y intercepts from the equation of a line
    • To find the x- intercept of the line, let y = 0 and solve for x .
    • To find the y- intercept of the line, let x = 0 and solve for y .
      x y
      0
      0
  • Graph a line using the intercepts
    1. Find the x- and y- intercepts of the line.
      • Let y = 0 and solve for x.
      • Let x = 0 and solve for y.
    2. Find a third solution to the equation.
    3. Plot the three points and then check that they line up.
    4. Draw the line.
  • Choose the most convenient method to graph a line
    1. Determine if the equation has only one variable. Then it is a vertical or horizontal line.
      x = a is a vertical line passing through the x- axis at a .
      y = b is a vertical line passing through the y- axis at b .
    2. Determine if y is isolated on one side of the equation. The graph by plotting points.
      Choose any three values for x and then solve for the corresponding y- values.
    3. Determine if the equation is of the form A x + B y = C , find the intercepts.
      Find the x- and y- intercepts and then a third point.

Practice makes perfect

Identify the Intercepts on a Graph

In the following exercises, find the x - and y - intercepts.

Find the x and y Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

x + y = −2

(−2,0),(0,−2)

Got questions? Get instant answers now!

x y = 5

(5,0),(0,−5)

Got questions? Get instant answers now!

x y = −3

(−3,0),(0,3)

Got questions? Get instant answers now!

x −3 y = 12

(12,0),(0,−4)

Got questions? Get instant answers now!

4 x y = 8

(2,0),(0,−8)

Got questions? Get instant answers now!

2 x + 5 y = 10

(5,0),(0,2)

Got questions? Get instant answers now!

3 x −2 y = 12

(4,0),(0,−6)

Got questions? Get instant answers now!

y = 1 3 x −1

(3,0),(0,−1)

Got questions? Get instant answers now!

y = 1 5 x + 2

(−10,0),(0,2)

Got questions? Get instant answers now!

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Choose the Most Convenient Method to Graph a Line

In the following exercises, identify the most convenient method to graph each line.

y = −3 x + 4

plotting points

Got questions? Get instant answers now!

y = 2 3 x −1

plotting points

Got questions? Get instant answers now!

y = −3

horizontal line

Got questions? Get instant answers now!

3 x −2 y = −12

intercepts

Got questions? Get instant answers now!

y = 1 4 x + 3

plotting points

Got questions? Get instant answers now!

Everyday math

Road trip Damien is driving from Chicago to Denver, a distance of 1,000 miles. The x -axis on the graph below shows the time in hours since Damien left Chicago. The y -axis represents the distance he has left to drive.

The graph shows the x y-coordinate plane. The x and y-axis each run from - to .  A line passes through the labeled points “ordered pair 0, 1000” and “ordered pair 15, 0”.

Find the x - and y - intercepts

Explain what the x - and y - intercepts mean for Damien.

(0,1,000),(15,0). At (0,1,000) he left Chicago 0 hours ago and has 1,000 miles left to drive. At (15,0) he left Chicago 15 hours ago and has 0 miles left to drive.

Got questions? Get instant answers now!

Road trip Ozzie filled up the gas tank of his truck and went on a road trip. The x -axis on the graph shows the number of miles Ozzie drove since filling up. The y -axis represents the number of gallons of gas in the truck’s gas tank.

The graph shows the x y-coordinate plane. The x and y-axis each run from - to .  A line passes through labeled points “ordered pair 0, 16” and “ordered pair 300, 0”.

Find the x - and y - intercepts.

Explain what the x - and y - intercepts mean for Ozzie.

Got questions? Get instant answers now!

Writing exercises

How do you find the x -intercept of the graph of 3 x −2 y = 6 ?

Answers will vary.

Got questions? Get instant answers now!

How do you find the y -intercept of the graph of 5 x y = 10 ?

Got questions? Get instant answers now!

Do you prefer to graph the equation 4 x + y = −4 by plotting points or intercepts? Why?

Answers will vary.

Got questions? Get instant answers now!

Do you prefer to graph the equation y = 2 3 x −2 by plotting points or intercepts? Why?

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
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
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.
Kimberly Reply
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.
August Reply
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