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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

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
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what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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absolutely yes
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it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
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for teaching engĺish at school how nano technology help us
Anassong
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
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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 ?
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for screen printed electrodes ?
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What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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On having this app for quite a bit time, Haven't realised there's a chat room in it.
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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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