2.7 Linear Inequalities in two variables Teacher- Mrs. Volynskaya

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2.7 Linear Inequalities in two variables Teacher-
Mrs. Volynskaya

• Standard SWBAT sketch the region defined by
  linear inequality

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Warm-up

• 1. Determine if 5 is a solution to
• 2. Graph the equation y x 2

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Overview

• Graphing Linear Inequalities
• Solid or Dotted
• Which Side to Shade
• Writing Inequalities from a graph

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Graphing Linear Inequalities in Two Variables

• How would you graph the equation x y 3?

x y 3 -x -x y -x 3 m -1 b 3
What happens if the changes to or ?
We get shading!!!
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?

• Graph x y 3

Pick a point not on the line to find out which
side to shade. If its true, shade same side. If
not, shade the opposite side!
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?

• Graph x y 3

What point do you want to pick?
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Solid or dashed?

• The lines can be graphed as a solid line or a
  dashed (dotted) line. When do you think its
  solid, and when is it dashed? Think about
  graphing points on a number line when is it open
  and when is it closed?
• lt or gt is
• or is

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Graphing Linear Inequalities

• Steps
• 1. Graph the equation (solve for y)
• 2. Draw a Dotted or Solid line
• 3. Pick a point not on a line (any point)
• 4. Shade the correct side
• True shade the same side
• False shade the opposite side

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Graph These

• y lt -2

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Graph These

• 2. -1 x y

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Graph These

• 3. x gt 4

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Graph These

• 4. x 3y 12

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Writing an Inequality

• Write an inequality for each graph.
• 5. 6.

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Writing an Inequality

• Write an inequality for each graph.
• 7. 8.

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Application

• 9. Suppose your budget for a party allows you to
  spend no more than 12 on peanuts and cashews.
  Peanuts cost 2/lb and cashews cost 4/lb. Find
  three possible combinations of peanuts and
  cashews you can buy.
• x number of pounds of peanuts
• y number of pounds of cashews
• 2x 4y 12