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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. In this chapter the student is shown how graphs provide information that is not always evident from the equation alone. The chapter begins by establishing the relationship between the variables in an equation, the number of coordinate axes necessary to construct its graph, and the spatial dimension of both the coordinate system and the graph. Interpretation of graphs is also emphasized throughout the chapter, beginning with the plotting of points. The slope formula is fully developed, progressing from verbal phrases to mathematical expressions. The expressions are then formed into an equation by explicitly stating that a ratio is a comparison of two quantities of the same type (e.g., distance, weight, or money). This approach benefits students who take future courses that use graphs to display information.The student is shown how to graph lines using the intercept method, the table method, and the slope-intercept method, as well as how to distinguish, by inspection, oblique and horizontal/vertical lines. Objectives of this module: be able to relate solutions to a linear equation to lines, know the general form of a linear equation, be able to construct the graph of a line using the intercept method, be able to distinguish, by their equations, slanted, horizontal, and vertical lines.


  • Solutions and Lines
  • General form of a Linear Equation
  • The Intercept Method of Graphing
  • Graphing Using any Two or More Points
  • Slanted, Horizontal, and Vertical Lines

Solutions and lines

We know that solutions to linear equations in two variables can be expressed as ordered pairs. Hence, the solutions can be represented by point in the plane. We also know that the phrase “graph the equation” means to locate the solution to the given equation in the plane. Consider the equation y 2 x = 3 . We’ll graph six solutions (ordered pairs) to this equation on the coordinates system below. We’ll find the solutions by choosing x -values (from 1 to + 4 ), substituting them into the equation y 2 x = 3 , and then solving to obtain the corresponding y -values . We can keep track of the ordered pairs by using a table.

y 2 x = 3

If x = Then y = Ordered Pairs
1 5 ( 1 , 5 )
0 3 ( 0 , 3 )
1 1 ( 1 , 1 )
2 1 ( 2 , 1 )
3 3 ( 3 , 3 )
4 5 ( 4 , 5 )

Total six points plotted for graphing the line y minus two x equals negative three. The coordinates of these points are negative one, negative five; zero, negative three; one, negative one; two, one; three, three; and four, five.

We have plotted only six solutions to the equation y 2 x = 3 . There are, as we know, infinitely many solutions. By observing the six points we have plotted, we can speculate as to the location of all the other points. The six points we plotted seem to lie on a straight line. This would lead us to believe that all the other points (solutions) also lie on that same line. Indeed, this is true. In fact, this is precisely why first-degree equations are called linear equations.

Linear equations produce straight lines

Line Linear

A graph of a line passing through six points with the coordinates negative one, negative five; zero, negative three; one, negative one; two, one; three, three; and four, five.

General form of a linear equation

General form of a linear equation in two variables

There is a standard form in which linear equations in two variables are written. Suppose that a , b , and c are any real numbers and that a and b cannot both be zero at the same time. Then, the linear equation in two variables

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.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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