# 3.2 Understanding how equations are represented on a graph

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## Understanding how equations are represented on a graph

ACTIVITY 1

To understand how equations can be represented on a graph

[LO 2.2, 2.5, 2.6]

E x ample : The equation y = 3 x + 2 tells one how the values of x and y are connected – it shows the relationship between two variables, x and y .

• For example, if x is 5, then y can be calculated from 3 × 5 + 2, giving 17. So, we substitute the value 5 for the x , and complete the calculation.
• The table shows some of the answers.

The point of making a table is that it gives us coordinates, which we can plot on a set of axes. From these we can draw a graph, which is a picture of the relationship between x and y.

1 In a group of 4 or 5 learners, complete the tables from the equations below. Each one should do a different table, and then discuss the answers and copy the others’ tables into your book. Below each table is a set of axes on which to draw the graph. All of these graphs will be straight lines, so you may connect the points you plot from each table.

2 In your group, discuss what you see in your graphs. Compare the graph with the equation. Here are a few suggestions for you to investigate:

2.1 What does the coefficient of x in the equation do to the graph? What happens when the coefficient is negative?

2.2 In 1.6 the table has only two columns. Is it necessary to have more than two columns if you know that the graph will be a straight line?

2.3 Compare 1.1 and 1.5 to see if you can find out what the constant does to the graph.

• The table summarises how equations, tables and graphs agree with one another. You have to memorise this information – you can’t work correctly with graphs if you don’t know the words
 Equation: x y Equation: Independent variable Dependent variable Flow diagram:: Input value Output value Table: First row Second row Coordinates: 1st coordinate 2nd coordinate Graph: x – axis y – axis Graph: Horizontal axis Vertical axis

ACTIVITY 2

To understand and apply all the characteristics of the straight-line graph

[LO 2.5]

1 In the previous activity you used equations to make tables from which graphs were drawn. One can also draw a graph from an equation without making a table. As we saw in graph 1.6 above, if we know that we have to draw a straight line, then two points on the graph paper are sufficient to enable us to draw the line. We don’t need a table if we have the equation of the straight line.

• In this section we will refer repeatedly to the six graphs in the previous e x ercise.
• First we have to examine the structure of the equation:

y = mx + c is the standard form of the equation:

• y is on the left of the equal sign, and y has no coefficient (which is the same as saying that its coefficient is 1 , which we don’t write)
• After the equal sign there may be one or two terms (compare equations 1.5 and 1.6 above). If there are two terms, then the term in x is written first – the x may have any number as a coefficient: positive, negative or fractional.
• In the standard form we write an m to stand for the coefficient. If the coefficient is 1 , then again we don’t write it.
• The c stands for a constant – any number that is not a variable: it can also be negative, positive or fractional.
• If we write y = mx + c then this is the general equation for all straight lines. But y = –3 x + 2 is the defining equation for a specific straight line.

#### Questions & Answers

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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
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
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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