Graphing Inequalities

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Graphing Inequalities

• Eric Hoffman
• Algebra II
• PLHS
• Sept. 2007

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Key Topics

• Graphing Inequalities to graph an inequality you
  graph boundary line then shade the appropriate
  region
• Boundary Line the line that is the boundary for
  the shaded region

Boundary Line
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Key Topics

• If the inequality is a or then the
  boundary line is solid
• If the inequality is a lt or gt then the
  boundary line is dashed

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Steps For Graphing an Inequality

• Step 1 Determine whether the boundary line is
  dashed or solid
• Step 2 Graph the boundary line
• Step 3 Choose a point on either side of the
  boundary line and check to see if the values
  satisfy the inequality
• Step 4 Shade the side of the boundary line that
  satisfies the inequality

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Graphing an Inequality

• Graph the inequality 2x 3y gt 6
• 3y gt -2x 6
• y gt (-2/3)x 2
• Graph y (-2/3)x 2
• Choose any point
• (3,3)
• 3 gt (-2/3)(3) 2
• 2 gt (-2) 2
• 2 gt 0

Tells us the boundary line is dashed
(3,3) is just a random point
This is true, so we shade the side of the
boundary line that this point is on
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Key Topics

• Graph the inequality 3y 6x 9
• y -2x 3
• Check point
• (2,1)
• 1 -2(2) 3
• 1 -1

y -2x 3
True, so shade this region
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Graphing Absolute Value Inequalities

• Same method as graphing regular inequalities
• The graph of the absolute value of a linear
  equation will always look like a V
• If you have trouble graphing absolute values,
  just plot points by picking different values for x

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Absolute Value Inequality

• There are basically two regions, region 1 is all
  the points where y is greater than, and region 2
  is all the points where y is less than

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y x 1
2
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Key Topics

• Graph
• y 3x 2
• Boundary line y 3x 2
• Choose a point (0,0)
• Choose another point (0,3)

(0,0) doesnt satisfy the inequality so you cant
shade the region that it is in
y 3x 2
(0,3) satisfies the inequality, so shade this
region
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Homework

• Pg. 98 14 28 even, 32 37 all
• 14 problems
• You will need graph paper (provided)