U2-S3-L5 Linear Inequalities

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U2-S3-L5 Linear Inequalities

• Essential Question
• How do you graph, write, and use linear
  inequalities?

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Linear Inequalities

• A solution to a linear inequality is any ordered
  pair that makes the inequality true.
• A linear inequality describes a region of a
  coordinate plane called a half plane.
• ALL points in the region are solutions

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Graphing Linear Inequalities

• How did we graph inequalities like x lt 5, x gt 9?
• To graph linear inequalities
• Use slope-intercept form (y mx b)
• Use a solid or dashed line
• Shade above or below the line

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Graphing Linear Inequalities
Linear Inequalities Shade ABOVE Shade BELOW
DASHED gt lt
SOLID gt lt
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Example 2 Graphing

1. Put in slope-intercept form
2. Plot the y-intercept
3. Use the slope (rise over run) to graph two more
   points
4. Connect with a dashed or solid line
5. Shade above or below the line

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Example 2 Graphing

1. Put in slope-intercept form
2. Plot the y-intercept
3. Use the slope (rise over run) to graph two more
   points
4. Connect with a dashed or solid line
5. Shade above or below the line

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Example 2 Practice
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Example 3 Application
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Example 4 Writing an Inequality

• To write an inequality from a graph,
• Identify the y-intercept
• Identify the slope
• Determine the inequality symbol

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Example 4 Practice
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Special Cases

• Horizontal Line
• y gt 5

• Vertical Line
• x lt -3

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REVIEW

1. How do you know if an ordered pair is not a
   solution of a linear inequality?
2. How can you check that you shaded the correct
   half-plane?
3. Can the reasonable solutions of a linear
   inequality include fractions and decimals? Why or
   why not?
4. How do you determine which inequality symbol to
   use when writing an inequality from a graph?

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SUMMARY

• Answer the essential question in detailed,
  complete sentences.
• How do you graph, write, and use linear
  inequalities?
• Write 3-5 Study Questions in the left column to
  correspond to the notes.