# 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.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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Alexandre
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
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?
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
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