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By the end of this section, you will be able to:
  • Recognize the relation between the solutions of an equation and its graph
  • Graph a linear equation by plotting points
  • Graph vertical and horizontal lines

Before you get started, take this readiness quiz.

  1. Evaluate: 3 x + 2 when x = −1 .
    If you missed this problem, review Multiply and Divide Integers .
  2. Solve the formula: 5 x + 2 y = 20 for y .
    If you missed this problem, review Solve a Formula for a Specific Variable .
  3. Simplify: 3 8 ( −24 ) .
    If you missed this problem, review Multiply and Divide Fractions .

Recognize the relation between the solutions of an equation and its graph

In Use the Rectangular Coordinate System , we found a few solutions to the equation 3 x + 2 y = 6 . They are listed in the table below. So, the ordered pairs ( 0 , 3 ) , ( 2 , 0 ) , ( 1 , 3 2 ) , ( 4 , 3 ) , are some solutions to the equation 3 x + 2 y = 6 . We can plot these solutions in the rectangular coordinate system as shown on the graph at right.

...

Notice how the points line up perfectly? We connect the points with a straight line to get the graph of the equation 3 x + 2 y = 6 . Notice the arrows on the ends of each side of the line. These arrows indicate the line continues.

...

Every point on the line is a solution of the equation. Also, every solution of this equation is a point on this line. Points not on the line are not solutions!

Notice that the point whose coordinates are ( 2 , 6 ) is on the line shown in [link] . If you substitute x = 2 and y = 6 into the equation, you find that it is a solution to the equation.

...

So ( 4 , 1 ) is not a solution to the equation 3 x + 2 y = 6 . Therefore the point ( 4 , 1 ) is not on the line.

This is an example of the saying,” A picture is worth a thousand words.” The line shows you all the solutions to the equation. Every point on the line is a solution of the equation. And, every solution of this equation is on this line. This line is called the graph of the equation 3 x + 2 y = 6 .

Graph of a linear equation

The graph of a linear equation A x + B y = C is a straight line.
  • Every point on the line is a solution of the equation.
  • Every solution of this equation is a point on this line.

The graph of y = 2 x 3 is shown below.

...

For each ordered pair decide

  1. Is the ordered pair a solution to the equation?
  2. Is the point on the line?

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

Substitute the x - and y -values into the equation to check if the ordered pair is a solution to the equation.


...

Plot the points A: ( 0 , 3 ) B: ( 3 , 3 ) C: ( 2 , 3 ) and D: ( 1 , 5 ) .
The points ( 0 , 3 ) , ( 3 , 3 ) , and ( 1 , 5 ) are on the line y = 2 x 3 , and the point ( 2 , 3 ) is not on the line.

...

The points which are solutions to y = 2 x 3 are on the line, but the point which is not a solution is not on the line.

Got questions? Get instant answers now!

The graph of y = 3 x 1 is shown.

For each ordered pair, decide

  1. is the ordered pair a solution to the equation?
  2. is the point on the line?
...
  1. ( 0 , 1 )
  2. ( 2 , 2 )
  3. ( 3 , 1 )
  4. ( 1 , 4 )
  1. yes yes
  2. no no
  3. no no
  4. yes yes
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Graph a linear equation by plotting points

There are several methods that can be used to graph a linear equation. The method we used at the start of this section to graph is called plotting points, or the Point-Plotting Method .

Let’s graph the equation y = 2 x + 1 by plotting points.

Questions & Answers

important of enocomic
Adu Reply
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Dennis Reply
division of labour can be defined as the separation of task to individuals in any economic system to specialize on it.
Ahmad
what is demand curve
Victoria Reply
demand curve is a downward sloping economic graph that shows the relationship between the price of product and the quantity of the product demanded.
Ahmad
What is demand
Frank Reply
It refers to the quantity of a commodity purchased in the market at a price and at a point of time.
Basanta
refers to amount of commodities a consumer is willing and able to buy at particular price within a period of time
Clifford
It is the ability and willingness a customer buys a product or service at a particular price, place and time while other things remaining constant or the same
kum
In which case is opportunity cost is zero
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where no alternative is available
Bhartendu
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Omar Reply
Adam Smith
Suraj
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Adam Smith
Francis
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Opana
Adam Smith
Basanta
What is monopoly
Mauthoor Reply
it an economic situation where one individual controls the essential commodities or value product for maximum profit
James
monopoly is a market situation in which there is only one producer of a good or service which has no close substitutes
eliano
is where only one person is solely the price taker
Francis
what is Monopoly
Dauda Reply
The word Monopoly is a Latin word. it is the combination of two words-Mono means single and Poly means seller. thus Monopoly means single seller. but this is not the full meaning of Monopoly. Monopoly must produce a product which does not have close substitute in the market.
Basanta
Monopoly is define as a firm in an industry with very high barriers to entry.
Favour
If close substitute is available, Monopoly will be a king without a crown.
Basanta
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Cbdishakur Reply
what are the differences between monopoly and.oligopoly
Onome Reply
what are the difference between monopoly and oligopoly
Cbdishakur
The deference between Monopoly and Oligopoly: Monopoly means:A single-firm-Industry producing and selling a product having no close business and Oligopoly means:A market structure where a few sellers compete with each other and each controls a significant portion of market .
Basanta
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Basanta
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hon
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Emakpor Reply
what is economic
Cbdishakur
the word economic was derived from the Greek word oikos (a house)and mein(to manage) which in effect meant managing a household with the limited funds available 🙂.
Basanta
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hon
An Enquiry into the nature and causes of wealth Nations, this book clearly defined what economic is🙂🙂🙏🙏 thank you...
Basanta
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Basanta
equilibrium is a situation in which economic forces such as demand and supply are balanced and in the absence of external influences,the value of economic variables will not change
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Emakpor
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Study
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shubham
so good night
hon
Why do people buy more grapes in December than in July?
lungi
because at time know money
Adu
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly 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
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Shanjida
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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 2

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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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