# 7.2 Plotting points in the plane  (Page 2/2)

 Page 2 / 2

## The coordinates determine distance and direction

A positive number means a direction to the right or up . A negative number means a direction to the left or down .

## Plotting points

Since points and ordered pairs are so closely related, the two terms are sometimes used interchangeably. The following two phrases have the same meaning:

1. Plot the point $\left(a,\text{\hspace{0.17em}}b\right)$ .
2. Plot the ordered pair $\left(a,\text{\hspace{0.17em}}b\right)$ .

## Plotting a point

Both phrases mean: Locate, in the plane, the point associated with the ordered pair $\left(a,\text{\hspace{0.17em}}b\right)$ and draw a mark at that position.

## Sample set a

Plot the ordered pair $\left(2,\text{\hspace{0.17em}}6\right)$ .

We begin at the origin. The first number in the ordered pair, 2, tells us we move 2 units to the right ( $+2$ means 2 units to the right) The second number in the ordered pair, 6, tells us we move 6 units up ( $+6$ means 6 units up).

## Practice set a

Plot the ordered pairs.

$\left(1,\text{\hspace{0.17em}}3\right),\text{\hspace{0.17em}}\left(4,\text{\hspace{0.17em}}-5\right),\text{\hspace{0.17em}}\left(0,\text{\hspace{0.17em}}1\right),\text{\hspace{0.17em}}\left(-4,\text{\hspace{0.17em}}0\right)$ .

(Notice that the dotted lines on the graph are only for illustration and should not be included when plotting points.)

## Exercises

Plot the following ordered pairs. (Do not draw the arrows as in Practice Set A.)
$\left(8,\text{\hspace{0.17em}}2\right),\text{\hspace{0.17em}}\left(10,\text{\hspace{0.17em}}-3\right),\text{\hspace{0.17em}}\left(-3,\text{\hspace{0.17em}}10\right),\text{\hspace{0.17em}}\left(0,\text{\hspace{0.17em}}5\right),\text{\hspace{0.17em}}\left(5,\text{\hspace{0.17em}}0\right),\text{\hspace{0.17em}}\left(0,\text{\hspace{0.17em}}0\right),\text{\hspace{0.17em}}\left(-7,\text{\hspace{0.17em}}-\frac{3}{2}\right)$ .

As accurately as possible, state the coordinates of the points that have been plotted on the following graph.

Using ordered pair notation, what are the coordinates of the origin?

$\text{Coordinates\hspace{0.17em}of\hspace{0.17em}the\hspace{0.17em}origin\hspace{0.17em}are}\left(0,0\right)$ .

We know that solutions to linear equations in two variables can be expressed as ordered pairs. Hence, the solutions can be represented as points in the plane. Consider the linear equation $y=2x-1$ . Find at least ten solutions to this equation by choosing $x\text{-values}$ between $-4$ and 5 and computing the corresponding $y\text{-values}$ . Plot these solutions on the coordinate system below. Fill in the table to help you keep track of the ordered pairs.

 $x$ $y$

Keeping in mind that there are infinitely many ordered pair solutions to $y=2x-1$ , speculate on the geometric structure of the graph of all the solutions. Complete the following statement:

The name of the type of geometric structure of the graph of all the solutions to the linear equation
$y=2x-1$ seems to be __________ .

Where does this figure cross the $y\text{-axis}$ ? Does this number appear in the equation $y=2x-1$ ?

Place your pencil at any point on the figure (you may have to connect the dots to see the figure clearly). Move your pencil exactly one unit to the right (horizontally). To get back onto the figure, you must move your pencil either up or down a particular number of units. How many units must you move vertically to get back onto the figure, and do you see this number in the equation $y=2x-1$ ?

Consider the $xy\text{-plane}$ .

Complete the table by writing the appropriate inequalities.

 I II III IV $x>0$ $x<0$ $x$ $x$ $y>0$ $y$ $y$ $y$

In the following problems, the graphs of points are called scatter diagrams and are frequently used by statisticians to determine if there is a relationship between the two variables under consideration. The first component of the ordered pair is called the input variable and the second component is called the output variable . Construct the scatter diagrams. Determine if there appears to be a relationship between the two variables under consideration by making the following observations: A relationship may exist if
1. as one variable increases, the other variable increases
2. as one variable increases, the other variable decreases

 I II III IV $x>0$ $x<0$ $x<0$ $x>0$ $y>0$ $y>0$ $y<0$ $y<0$

A psychologist, studying the effects of a placebo on assembly line workers at a particular industrial site, noted the time it took to assemble a certain item before the subject was given the placebo, $x$ , and the time it took to assemble a similar item after the subject was given the placebo, $y$ . The psychologist's data are

 $x$ $y$ 10 8 12 9 11 9 10 7 14 11 15 12 13 10

The following data were obtained in an engineer’s study of the relationship between the amount of pressure used to form a piece of machinery, $x$ , and the number of defective pieces of machinery produced, $y$ .

 $x$ $y$ 50 0 60 1 65 2 70 3 80 4 70 5 90 5 100 5

Yes, there does appear to be a relation.

The following data represent the number of work days missed per year, $x$ , by the employees of an insurance company and the number of minutes they arrive late from lunch, $y$ .

 $x$ $y$ 1 3 6 4 2 2 2 3 3 1 1 4 4 4 6 3 5 2 6 1

A manufacturer of dental equipment has the following data on the unit cost (in dollars), $y$ , of a particular item and the number of units, $x$ , manufactured for each order.

 $x$ $y$ 1 85 3 92 5 99 3 91 4 100 1 87 6 105 8 111 8 114

Yes, there does appear to be a relation.

## Exercises for review

( [link] ) Simplify ${\left(\frac{18{x}^{5}{y}^{6}}{9{x}^{2}{y}^{4}}\right)}^{5}$ .

( [link] ) Supply the missing word. An is a statement that two algebraic expressions are equal.

equation

( [link] ) Simplify the expression $5xy\left(xy-2x+3y\right)-2xy\left(3xy-4x\right)-15x{y}^{2}$ .

( [link] ) Identify the equation $x+2=x+1$ as an identity, a contradiction, or a conditional equation.

( [link] ) Supply the missing phrase. A system of axes constructed for graphing an equation is called a .

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
Abigail
Do somebody tell me a best nano engineering book for beginners?
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
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Please keep in mind that it's not allowed to promote any social groups (whatsapp, facebook, etc...), exchange phone numbers, email addresses or ask for personal information on QuizOver's platform.