MAT 150 Unit 15

1
MAT 150 Unit 15

• Chapter 9 1
• Graphing Linear Equations

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CONTENTS

• Rene Descartes
• The Axis
• The Origin
• Ordered Pair
• The Coordinate Plane
• Quadrants
• Coordinates

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René Descartes1596-1650

• René Descartes was a French philosopher,
  scientist, and mathematician, born in1596 and
  died in 1650.

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The Coordinate Plane

• The Coordinate Plane is formed by two number
  lines intersecting at right angles

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Axis

• Each Number Line is called an axis
• x-Axis The x-axis is the horizontal axis.
• y-Axis The y-axis is the vertical axis.

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Quadrants

• The x and y axes divide the coordinate plane into
  four sections called quadrants.

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The Origin

• The origin is the place where the x-axis and the
  y-axis intersect (0, 0)

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Ordered Pair

• Ordered pairs are numbers represented in
  parenthesis by the x value followed by the y
  value. Pairs because there are 2 and ordered
  because the order is important.

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Coordinates

• Coordinates of a point are the numbers in its
  ordered pair.
• The first number in an ordered pair (x, y) is
  the x-coordinate.
• The second number in an ordered pair (x, y) is
  the y-coordinate.

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Line as a Series of Points

• A line is made up of an infinite, continuous set
  of points. A line is created when two or more
  sets of points are joined.

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Graphing Lines

• Graphing by a table of values
• y x 2
• Make a table
• Select values for x, the independent variable,
  substitute them in the expression x 2 and you
  get the values for y, the dependent variable. It
  is called dependent because it depends on the
  value of x.

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Graphing Lines

• The table would look like this
• So this would yield the following ordered pairs
• (0, -2), (1, -1), (2, 0), (3,
  1)
• These are all SOLUTIONS to the equation

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Graphing Lines

• (0, -2), (1, -1), (2, 0), (3, 1)

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Graphing Lines

• Some equations are more difficult, like
• 2x y 5
• So always solve the equation for y, so it reads y
  
• 2x y 5
• 2x 2x
  subtract 2x
• y 2x 5
• Then make your table and substitute a minimum of
  3 values for x.

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Graphing Lines

• The table would look like this
• So this would yield the following ordered pairs
• (0, 5), (1, 3), (2, 1), (3,
  1)
• These are all SOLUTIONS to the equation

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Graphing Lines

• (0, 5), (1, 3), (2, 1), (3, 1)

(0, 5)
(1, 3)
(2, 1)
(3, -1)