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y = 7 x . In this case m = 7 and b = 0 since we can write y = 7 x as y = 7 x + 0.

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The following equations are not in slope-intercept form:

2 y = 4 x 1. The coefficient of y is 2. To be in slope-intercept form, the coefficient of y must be 1.

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y + 4 x = 5. The equation is not solved for y . The x and y appear on the same side of the equal sign .

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y + 1 = 2 x . The equation is not solved for y .

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Practice set a

The following equation are in slope-intercept form. In each case, specify the slope and y -intercept .

y = 2 x + 7 ; m = b =

m = 2 , b = 7

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y = 4 x + 2 ; m = b =

m = 4 , b = 2

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y = 5 x 1 ; m = b =

m = 5 , b = 1

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y = 2 3 x 10 ; m = b =

m = 2 3 , b = 10

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y = 5 8 x + 1 2 ; m = b =

m = 5 8 , b = 1 2

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y = 3 x ; m = b =

m = 3 , b = 0

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Slope and intercept

When the equation of a line is written in slope-intercept form, two important properties of the line can be seen: the slope and the intercept . Let's look at these two properties by graphing several lines and observing them carefully.

Sample set b

Graph the line y = x 3 .

x y ( x , y )
0 3 ( 0 , 3 )
4 1 ( 4 , 1 )
2 5 ( 2 , 5 )

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

Looking carefully at this line, answer the following two questions.

At what number does this line cross the y -axis ? Do you see this number in the equation?

The line crosses the y -axis at - 3 .

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Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

After moving horizontally one unit to the right, we must move exactly one vertical unit up. This number is the coefficient of x .

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Graph the line y = 2 3 x + 1 .

x y ( x , y )
0 1 ( 0 , 1 )
3 3 ( 3 , 3 )
3 1 ( 3 , 1 )

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

Looking carefully at this line, answer the following two questions.

At what number does this line cross the y -axis ? Do you see this number in the equation?

The line crosses the y -axis at + 1 .

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Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

After moving horizontally one unit to the right, we must move exactly 2 3 unit upward. This number is the coefficient of x .

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Practice set b

Graph the line y = 3 x + 4 .

x y ( x , y )
0
3
2

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

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Looking carefully at this line, answer the following two questions.

At what number does the line cross the y -axis ? Do you see this number in the equation?

The line crosses the y -axis at + 4 . After moving horizontally 1 unit to the right, we must move exactly 3 units downward.

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Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

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

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In the graphs constructed in Sample Set B and Practice Set B, each equation had the form y = m x + b . We can answer the same questions by using this form of the equation (shown in the diagram).

A graph of a line sloped up and to the right in a first quadrant labeled with the equation y equal to mx plus b and intersecting y axis at point with coordinates zero, b. Lines illustrating an upward change of m units and a horizontal change of one unit to the right.

y -intercept

At what number does the line cross the y -axis ? Do you see this number in the equation?

In each case, the line crosses the y -axis at the constant b . The number b is the number at which the line crosses the y -axis , and it is called the y -intercept . The ordered pair corresponding to the y -intercept is ( 0 , b ) .

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Place your pencil at any point on the line. Move your pencil exactly one unit horizontally to the right. Now, how many units straight up or down must you move your pencil to get back on the line? Do you see this number in the equation?

To get back on the line, we must move our pencil exactly m vertical units.

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Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
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appreciation
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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,
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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)
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What is different between quantity demand and demand?
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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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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.
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What do you think is more important to focus on when considering inequality ?
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sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
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it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
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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 .
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Answer
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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
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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
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types of unemployment
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What is the difference between perfect competition and monopolistic competition?
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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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