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5 x + y = 10

  1. ( 5 , 1 )
  2. ( 2 , 0 )
  3. ( 4 , −10 )

,

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y = 6 x 2

  1. ( 1 , 4 )
  2. ( 1 3 , 0 )
  3. ( 6 , −2 )
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Complete a Table of Solutions to a Linear Equation in Two Variables

In the following exercises, complete the table to find solutions to each linear equation.

y = 4 x 1

x y ( x , y )
0
1
−2
x y ( x , y )
0 −1 ( 0 , −1 )
1 3 ( 1 , 3 )
−2 −9 ( −2 , −9 )
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y = 1 2 x + 3

x y ( x , y )
0
1
−2
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x + 2 y = 5

x y ( x , y )
0
1
−1
x y ( x , y )
5 0 ( 5 , 0 )
1 2 ( 1 , 2 )
−1 3 ( −1 , 3 )
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3 x 2 y = 6

x y ( x , y )
0
0
−2
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Find Solutions to a Linear Equation in Two Variables

In the following exercises, find three solutions to each linear equation.

x + y = 3

Answers will vary.

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y = 3 x + 1

Answers will vary.

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Graphing Linear Equations

Recognize the Relation Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide

  1. if the ordered pair is a solution to the equation.
  2. if the point is on the line.

y = x + 4

  1. ( 0 , 4 )
  2. ( −1 , 3 )
  3. ( 2 , 2 )
  4. ( −2 , 6 )
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0,  4” and “ordered pair 4, 0”.

  1. yes no yes yes
  2. yes no yes yes

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y = 2 3 x 1

  1. ( 0 , −1 )
  2. ( 3 , 1 )
  3. ( −3 , −3 )
  4. ( 6 , 4 )
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0,  -1” and “ordered pair 3, 1”.
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Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

Graph Vertical and Horizontal lines

In the following exercises, graph the vertical or horizontal lines.

Graphing with Intercepts

Identify the Intercepts on a Graph

In the following exercises, find the x - and y -intercepts .

Find the Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

x y = −1

(−1,0) (0,1)

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Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Choose the Most Convenient Method to Graph a Line

In the following exercises, identify the most convenient method to graph each line.

y = −3

horizontal line

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y = 3 4 x 1

plotting points

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Understand Slope of a Line

Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

In the following exercises, model each slope. Draw a picture to show your results.

Find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

Find the Slope of Horizontal and Vertical Lines

In the following exercises, find the slope of each line.

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

( −1 , −1 ) , ( 0 , −5 )

−4

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( 3 , 5 ) , ( 4 , −1 )

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( −5 , −2 ) , ( 3 , 2 )

1 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 = 1 3


The graph shows the x y-coordinate plane. The x-axis runs from -6 to 6. The y-axis runs from -4 to 2. A line passes through the points “ordered pair -3,  4” and “ordered pair 1, 3”.

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Solve Slope Applications

In the following exercise, solve the slope application.

A roof has rise 10 feet and run 15 feet. What is its slope?

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Chapter practice test

Plot and label these points:

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


The graph shows the x y-coordinate plane. The axes extend from -6 to 6. a is plotted at 2, 5, b at -1, -3, c at -4, 0, d at 3, -5, and e at -2,1.

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Name the ordered pair for each point shown.

The graph shows the x y-coordinate plane. The axes extend from -7 to 7. A is plotted at -4, 1, B at 3, 2, C at 0, -2, D at -1, -4, and E at 4,-3.
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Find the x -intercept and y -intercept on the line shown.

 The graph shows the x y-coordinate plane. The x-axis runs from -7 to 7. The y-axis runs from -7 to 7. A line passes through the points “ordered pair 4,  0” and “ordered pair 0, -2”.

(4,0), (0,−2)

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Find the x -intercept and y -intercept of the equation 3 x y = 6 .

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Is ( 1 , 3 ) a solution to the equation x + 4 y = 12 ? How do you know?

no; 1 + 4 · 3 ≠ 12

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Complete the table to find four solutions to the equation y = x + 1 .

x y ( x , y )
0
1
3
−2
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Complete the table to find three solutions to the equation 4 x + y = 8

x y ( x , y )
0
0
3
x y ( x , y )
0 8 ( 0 , 8 )
2 0 ( 2 , 0 )
3 −4 ( 3 , −4 )
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In the following exercises, find three solutions to each equation and then graph each line.

In the following exercises, find the slope of each line.

Use the slope formula to find the slope of the line between ( 0 , −4 ) and ( 5 , 2 ) .

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Find the slope of the line y = 2 .

0

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Graph the line passing through ( 1 , 1 ) with slope m = 3 2 .

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A bicycle route climbs 20 feet for 1,000 feet of horizontal distance. What is the slope of the route?

1 50

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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
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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
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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
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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
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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
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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
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_Adnan
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ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
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skin
Asiina
skin,Oral,Nasal,GIt
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all
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by fussion
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part of a tissue or an organ being wounded or bruised.
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Micheal Reply
Binomial nomenclature
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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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