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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. 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.

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( [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

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( [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.

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( [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 )

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

straight line

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

general form

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

slope-intercept

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( [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.

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( [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

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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

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

no slope; vertical line at  x = 2

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( [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 )

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

rise

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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

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

y = 3 2 x + 4 3

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

y = 2 3 x + 8 3

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

y = 7 x

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

y = 1 3 x + 1 3

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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.

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( [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.

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( [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.

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Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
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Venny Reply
how is the graph works?I don't fully understand
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information
Eliyee
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WARKISA
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Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
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Shukri
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Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
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Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
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Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
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Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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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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