<< Chapter < Page Chapter >> Page >
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. This module contains the proficiency exam for the chapter "Graphing Linear Equations and Inequalities in One and Two Variables".

Proficiency exam

For the following problems, construct a coordinate system and graph the inequality.

( [link] ) 6 x + 4 > 14

x < 3

A number line labeled x with arrows on each end, labeled from negative three to four, in increments of one. There is an open circle at three. A dark line is orginating from this circle and heading  towards the left of three.

Got questions? Get instant answers now!

( [link] ) 8 < x + 6 4

14 < x 10

A number line labeled x with arrows on each end, labeled at negative fourteen and negative ten. There is a closed circle at negative ten and an open circle at negative fourteen. These circles are connected by a black line

Got questions? Get instant answers now!

( [link] ) Plot the ordered pairs ( 3 , 1 ) , ( 2 , 4 ) , ( 0 , 5 ) , ( 2 , 2 ) .

An xy-plane with gridlines, labeled negative five and five on the both axes.

Total four points plotted in an xy-coordinate plane. The coordinates of these points are negative two, negative two; negative two, four; zero, five and three, one.

Got questions? Get instant answers now!

( [link] ) As accurately as possible, label the coordinates of the points that have been plotted on the graph.

Total four points plotted in an xy plane. The coordinates of these points are negative three, zero; zero, one; three, three and two, negative three.

( 0 , 1 ) , ( 3 , 3 ) , ( 3 , 0 ) , ( 2 , 3 )

Got questions? Get instant answers now!

( [link] ) What is the geometric structure of the graph of all the solutions to the equation 2 y + 3 x = 4 ?

straight line

Got questions? Get instant answers now!

( [link] ) In what form is the linear equation in two variables a x + b y = c ?

general form

Got questions? Get instant answers now!

( [link] ) In what form is the linear equation in two variables y = m x + b ?

slope-intercept

Got questions? Get instant answers now!

( [link] ) If an ordered pair is a solution to a linear equation in two variables, where does it lie geometrically?

It lies on the line.

Got questions? Get instant answers now!

( [link] ) Consider the graph of y = 2 7 x + 16 . If we were to place our pencil at any point on the line and then move it horizontally 7 units to the right, how many units and in what direction would we have to move our pencil to get back on the line?

2 units up

Got questions? Get instant answers now!

For the following two problems, find the slope, if it exists, of the line containing the following points.

( [link] ) ( 6 , 1 ) and ( 0 , 8 )

3 2

Got questions? Get instant answers now!

( [link] ) ( 2 , 8 ) and ( 2 , 10 )

no slope; vertical line at  x = 2

Got questions? Get instant answers now!

( [link] ) Determine the slope and y intercept of the line 3 y + 2 x + 1 = 0 .

slope = 2 3 , y -intercept is ( 0 , 1 3 )

Got questions? Get instant answers now!

( [link] ) As we look at a graph left to right, do lines with a positive slope rise or decline?

rise

Got questions? Get instant answers now!

For the following problems, find the equation of the line using the information provided. Write the equation in slope-intercept form.

( [link] ) Slope = 4, y -intercept = -3 .

y = 4 x 3

Got questions? Get instant answers now!

( [link] ) Slope = 3 2 , y -intercept = 4 3 .

y = 3 2 x + 4 3

Got questions? Get instant answers now!

( [link] ) slope = 2 3 , passes through ( 1 , 2 ) .

y = 2 3 x + 8 3

Got questions? Get instant answers now!

( [link] ) slope = 7, passes through (0, 0) .

y = 7 x

Got questions? Get instant answers now!

( [link] ) passes through the points ( 5 , 2 ) and ( 2 , 1 ) .

y = 1 3 x + 1 3

Got questions? Get instant answers now!


For the following problems, graph the equation of inequality.

( [link] - [link] ) y = 1 3 x 2

An xy-plane with gridlines, labeled negative five and five on the both axes.

y = 1 3 x 2

A graph of a line passing through two points with coordinates zero, negative two and three, negative one.

Got questions? Get instant answers now!

( [link] - [link] ) 4 ( x + y ) = 8

An xy-plane with gridlines, labeled negative five and five on the both axes.

4 ( x + y ) = 8

A graph of a line passing through four points with coordinates negative two, four; zero, two; two, zero; and four, negative two.

Got questions? Get instant answers now!

( [link] ) Reading only from the graph, determine the equation of the line.

A graph of a line sloped up and to the left.

y = 1 3 x + 3

A graph of a line passing through two points with coordinates negative three, four and three, two.

Got questions? Get instant answers now!

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask