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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

it is the relatively stable flow of income
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what is circular flow of income
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branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
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is gdp a reliable measurement of wealth
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introduction to econometrics
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Tom
Why is unemployment rate never zero at full employment?
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bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
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Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
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discus major problems of macroeconomics
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what is the problem of macroeconomics
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Economic growth Stable prices and low unemployment
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what is inflation
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increase in general price levels
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Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
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how to calculate actual output?
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how to calculate the equilibrium income
Beshir
Criteria for determining money supply
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who we can define macroeconomics in one line
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Aggregate demand
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C=k100 +9y and i=k50.calculate the equilibrium level of output
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A unit of account is something that can be used to value goods and services and make calculations
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I want to know how can we define macroeconomics in one line
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it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
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hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
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if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
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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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