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( −3 , 3 ) , ( 2 , −5 )

8 5

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( −2 , 4 ) , ( 3 , −1 )

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( −1 , −2 ) , ( 2 , 5 )

7 3

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( −2 , −1 ) , ( 6 , 5 )

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( 4 , −5 ) , ( 1 , −2 )

−1

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( 3 , −6 ) , ( 2 , −2 )

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Graph a Line Given a Point and the Slope

In the following exercises, graph the line given a point and the slope.

( −3 , 4 ) ; m = 3 2


The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair -3, 4” and “ordered pair -1, 1”.

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( −2 , 5 ) ; m = 5 4

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( −1 , −4 ) ; m = 4 3


The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair 2,0” and “ordered pair -1, -4”.

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( −3 , −5 ) ; m = 3 2

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Solve Slope Applications

In the following exercises, solve these slope applications.

Slope of a roof A fairly easy way to determine the slope is to take a 12-inch level and set it on one end on the roof surface. Then take a tape measure or ruler, and measure from the other end of the level down to the roof surface. You can use these measurements to calculate the slope of the roof. What is the slope of the roof in this picture?

The figure shows a wood board at a diagonal representing a side-view slice of a pitched roof. A vertical line segment with arrows on both ends measures the vertical change in height of the roof and is labeled “4 inches”. A level tool is in a horizontal position above the board and above it is a line segment with arrows on both ends labeled “12 inches”.

1 3

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What is the slope of the roof shown?

The figure shows a  diagonal side-view slice of a pitched roof. A ruler in vertical position is at the bottom of the roof segment and shows unit labels 1 through 8 and extends one further unit. A second ruler starts at the “7” label of the vertical ruler and extends horizontally until it hits the rising roof. The horizontal ruler has unit labels 1 through 11 and extends one further unit.
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Road grade A local road has a grade of 6% . The grade of a road is its slope expressed as a percent.

  1. Find the slope of the road as a fraction and then simplify the fraction.
  2. What rise and run would reflect this slope or grade?

3 50 rise = 3 ; run = 50

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Highway grade A local road rises 2 feet for every 50 feet of highway.

  1. What is the slope of the highway?
  2. The grade of a highway is its slope expressed as a percent. What is the grade of this highway?
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Everyday math

Wheelchair ramp The rules for wheelchair ramps require a maximum 1 inch rise for a 12 inch run.

  1. How long must the ramp be to accommodate a 24-inch rise to the door?
  2. Draw a model of this ramp.

  1. 288 inches (24 feet)
  2. Models will vary.

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Wheelchair ramp A 1-inch rise for a 16-inch run makes it easier for the wheelchair rider to ascend the ramp.

  1. How long must the ramp be to easily accommodate a 24-inch rise to the door?
  2. Draw a model of this ramp.
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Writing exercises

What does the sign of the slope tell you about a line?

Answers will vary.

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How does the graph of a line with slope m = 1 2 differ from the graph of a line with slope m = 2 ?

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Why is the slope of a vertical line undefined?

Answers will vary.

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Explain how you can graph a line given a point and its slope.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Chapter review exercises

Use the Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

  1. ( −1 , −5 )
  2. ( −3 , 4 )
  3. ( 2 , −3 )
  4. ( 1 , 5 2 )

  1. III
  2. II
  3. IV
  4. I

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  1. ( 3 , −2 )
  2. ( −4 , −1 )
  3. ( −5 , 4 )
  4. ( 2 , 10 3 )
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Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 5, 3, “b” at 2, -1, “c” at -3,-2, and “d” at -1,4.

  1. (5,3)
  2. (2,−1)
  3. (−3,−2)
  4. (−1,4)

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The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 2, 0, “b” at 0, -5, “c” at -4,0, and “d” at 0,3.

  1. (2,0)
  2. (0,−5)
  3. (−4,0)
  4. (0,3)

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Verify Solutions to an Equation in Two Variables

In the following exercises, find the ordered pairs that are solutions to the given equation.

Questions & Answers

Would you expect the kinked demand curve to be more extreme (like a right angle) or less extreme (like a normal demand curve) if each firm in the cartel produces a near-identical product like OPEC and petroleum? What if each firm produces a somewhat different product?
James Reply
no
Sadaf
what is supply
Mizta Reply
what is opportunity cost
Mizta
The opportunity gained interms of opportunity lost is known as opportunity cost Or The second best alternative use of resources
Mir
forgone alternative: like forgoing Something our of two to buy one
Tam-Waribo
what is macro economic s
Addo Reply
macroeconomics is the study of economic as a whole level.
Gafar
meaning of positive science
Sumit Reply
positive science it is focused on facts and cause and effect and behavioural relationship and include developmental testing in economic theoreis.
Gafar
what is inflation
Sama Reply
inflation is the general price increase of goods and services in an economy.
tesfie
Inflation is the persistent rise in the general price level
T-Max
inflation is characterized by increase in the general price of goods and services. when there is too much money in circulation. increase in demand of goods pursuing fewer goods. when purchasing power of money decreases .
Ejikeme
inflation is the persistent rise general price level
Habeeb
inflation is the persistent increase in price
Machall
hi
Rafiu
yes
boston
hi
Ayaan
how are you
Ayaan
increase in the general level of price...
sade
what is deflation
Sele
is the gradual decrease of currency exchange in a country.
Gafar
why ecnomics important ? give answer plz
Saifullah
Because is a field of science study that reflects on our day to day activities with human behavior.
ANSU
different between demand and quantity demand
Farhan Reply
No difference
MansoorAfghan
demand is the overall demand for it
MansoorAfghan
actually theres no difference
MansoorAfghan
quantity demanded is used in Equilibrium of d and s
MansoorAfghan
for evrything else u use deman
MansoorAfghan
the difference of it is that when demand simply denotes the willingness and a person's ability to purchase. And as against quantity demand represent the amount of an economic good or services desire by a consumer at a fixed price .☺
Gafar
how to calculate inflation
Richard Reply
Explain the factors that have led to high quantity demanded
Ogwang Reply
price of the product increase of price substitute product as people shift to cheap one
Black
what are the methods used by trade union to increase wages of their members?
Black Reply
strike
Pearl
the size of the commodity
Mensah
increase demand of labour decrease supply of labour
Black
I do support your answer Jackel.
keshav
but how do they do it?
Black
by increasing more labour and reduced the suppliers
Mensah
they can not increase labour, they increase demand of labour.
Black
how do they increase demand for labor?
Black
by analyzing the market equilibrium , cost reduction and cost control , savings in time .
yash
decreasing supply of labour are achieved through training and certification that require for you to employed, you must have certificate, also trade union encouraged government to restrict migration into the country causing shortage of labour supply. Note that the aim of union is to enhance life
Black
objective of union: better working conditions, liveable wage, protect member from unfair treatment which are done through negotiations betweens representative and management. known as collective bargaining.
Black
what is the nature of economics?
Tyscar Reply
economics is a social science since it seeks to solve social problem of scarcity
Jamal
main concerns is the decision individuals make on the allocation of scarce resources among the competing wants
Black
in the short run firm produce a positive as long as the price is larger than what?
yoel Reply
what is economic
Bah Reply
economics is the study of managing the resources in order to maximize the needs and satisfy the wants to a great extent in a regulated set-up..
Muhammad
One explanation for deviation when there is no impact on balance of trade
Shaneel
economic s is a social science that deals with human behavior as a relationship between ends and scarce means which has alternative uses
Derokiz
economic is a study of mankind in ordinary business of life
FIDELIS
economics it is the study of social science that deals with human behaviour as relationship between ends and scarce means which have alternative uses
salam
Economic is the use of scarce recourses to attain economic dough effectively and efficiently.
Addo
economics is the study of how humans make decisions in the face of scarcity. Eg. family decision, individual decision, and societal decision.
Gafar
what is diminishing returns
Blessed Reply
what is the difference between calculus linear equation and derivative?
Bti
whats inferior goods?
jaamac Reply
Good having low quality , also known as giffin goods. When income increases people shift to better quality goods . Hence having a negative effect on inferior goods rather than positive relation ( ie when income increases demand increases but not in case of inferior goods ) example wheat and bajra .
yash
What do u understand by the word ENDS in professor Lord L C Robinson definition of Economics?
Kaba Reply
I understand that ENDS is the unlimited needs of human. But we have limited resources to achieve our unlimited needs/wants. Thank you.
Midhun
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Good
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Beverly Reply
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo Reply
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Mapo Reply
Berger describes sociologists as concerned with
Mueller Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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