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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 more familiar with the general form of a line, be able to recognize the slope-intercept form of a line, be able to interpret the slope and intercept of a line, be able to use the slope formula to find the slope of a line.

Overview

  • The General Form of a Line
  • The Slope-Intercept Form of a Line
  • Slope and Intercept
  • The Formula for the Slope of a Line

The general form of a line

We have seen that the general form of a linear equation in two variables is a x + b y = c (Section [link] ). When this equation is solved for y , the resulting form is called the slope-intercept form. Let's generate this new form.

a x + b y = c Subtract a x from both sides . b y = a x + c Divide b o t h sides by b b y b = a x b + c b b y b = a x b + c b y = a x b + c b y = a x b + c b

This equation is of the form y = m x + b if we replace a b with m and constant c b with b . ( Note: The fact that we let b = c b is unfortunate and occurs beacuse of the letters we have chosen to use in the general form. The letter b occurs on both sides of the equal sign and may not represent the same value at all. This problem is one of the historical convention and, fortunately, does not occur very often.)

The following examples illustrate this procedure.

Solve 3 x + 2 y = 6 for y .

3 x + 2 y = 6 Subtract 3 x from both sides . 2 y = 3 x + 6 Divide both sides by 2 . y = 3 2 x + 3

This equation is of the form y = m x + b . In this case, m = - 3 2 and b = 3 .

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Solve - 15 x + 5 y = 20 for y .

15 x + 5 y = 20 5 y = 15 x + 20 y = 3 x + 4

This equation is of the form y = m x + b . In this case, m = 3 and b = 4 .

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Solve 4 x - y = 0 for y .

4 x y = 0 y = 4 x y = 4 x

This equation is of the form y = m x + b . In this case, m = 4 and b = 0 . Notice that we can write y = 4 x as y = 4 x + 0 .

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The slope-intercept form of a line

The slope-intercept form of a line y = m x + b

A linear equation in two variables written in the form y = m x + b is said to be in slope-intercept form.

Sample set a

The following equations are in slope-intercept form:

y = 6 x 7. In this case m = 6 and b = 7.

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y = 2 x + 9. In this case m = 2 and b = 9.

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y = 1 5 x + 4.8 In this case m = 1 5 and b = 4.8.

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Questions & Answers

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 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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
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
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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