Graphing%20Linear%20Equations%20in%20Two%20Variables

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Graphing Linear Equations in Two Variables
Section 8.4
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Linear Equation in Two Variables

• A linear equation in two variables is an equation
  that can be written in the form
• ax by c
• where a, b, and c are numbers, and a
  and b are not both 0.
• Examples
• 3x 2y 6 y 8 3x 4

Martin-Gay, Prealgebra, 5ed
3
Graphing Linear Equations by Plotting Points

• Every linear equation in two variables has
  infinitely many ordered-pair solutions. Since it
  is impossible to list every solution, we graph
  the solutions instead.
• The pattern described by the solutions of a
  linear equation makes seeing the solutions
  possible by graphing because all the solutions of
  a linear equation in two variables correspond to
  points on a single straight line.
• If we plot a few of these points and draw the
  straight line connecting them, we have a complete
  graph of all the solutions.

Martin-Gay, Prealgebra, 5ed
4
To graph the equation x y 5, we plot a few
ordered-pair solutions, say (2,3), (0,5), and
(-1, 6). Then we connect the points.
y
(0,5)
(- 1,6)
5
4
(2,3)
3
2
1
x
1
2
3
4
5
-1
-2
-3
- 4
- 5
Martin-Gay, Prealgebra, 5ed
5
To Graph a Linear Equation in Two Variables

• Find three ordered-pair solutions.
• Graph the solutions.
• Draw a line through the plotted points.

Martin-Gay, Prealgebra, 5ed
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To Find an Ordered-Pair Solution of an Equation

• Choose either an x-value or y-value of the
  ordered pair.
• Complete the ordered pair by replacing the
  variable with the chosen value and solving for
  the unknown variable.

Martin-Gay, Prealgebra, 5ed
7
All three points should fall on the same straight
line. If not, check your ordered-pair solutions
for a mistake, since every linear equation is a
line.
Martin-Gay, Prealgebra, 5ed
8
Horizontal Lines/Vertical Lines
y b
x a
Martin-Gay, Prealgebra, 5ed