2.8 Graphing Linear Inequalities

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2.8 Graphing Linear Inequalities

• Algebra 2
• Mrs. Spitz
• Fall 2006

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Objectives

• Draw graphs of inequalities in two variables, and
• Write an inequality to solve problems.

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Assignment

• pp. 94-9513-28 all

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Introduction

• When graphing inequalities, the boundaries you
  draw may be solid or dashed. If the inequality
  uses the symbol or , which may include
  equality, the boundary will be solid. Otherwise,
  it will be dashed. After graphing the boundary,
  you must determine which region is to be shaded.

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Introduction

• Test a point on one side of the line. If the
  ordered pair satisfied the inequality, that
  region contains solutions to the inequality. If
  the ordered pair does not satisfy the inequality,
  the other region is the solution.

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Chalkboard examples

1. Graph y lt 3.

1. Graph y x

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Chalkboard examples

1. Graph

1. Graph y lt 3x 1

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Chalkboard examples

1. Graph y x 1

1. Graph 3x 4y

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Ex. 1 Graph 2y 5 8.
x-intercept
y-intercept

• The boundary will be the graph of 2y 5 8.
  Use x and y intercepts to graph the boundary more
  easily.

• Graph the x and y intercepts on a coordinate
  graphing plane.
• Draw a solid line connecting these two
  intercepts. This is the boundary.

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Now graph/shade

• Now test a point.
• Try (2,0)

The region that contains (2, 0) should be shaded.
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Ex. 2 Graph y gt x - 1.
When x 0

• The absolute value has two conditions to consider
• y gt -x 1

When x lt 0
y gt -x -1
y gt x -1

• Graph each inequality for the specified values
  of x. The lines will be dashed.

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Now graph/shade

• Now test a point.
• Try (0,0)

The region that contains (0, 0) should be shaded.