2'6 Graphing linear Inequalities in 2 Variables

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2.6 Graphing linear Inequalities in 2 Variables

• p. 108

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Checking Solutions

• An ordered pair (x,y) is a solution if it makes
  the inequality true.
• Are the following solutions to
• 3x 2y 2
• (0,0) (2,-1) (0,2)

3(0) 2(2) 2 4 2 Is a solution
3(2) 2(-1) 2 4 2 Is a solution
3(0) 2(0) 2 0 2 Not a solution
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To sketch the graph of a linear inequality

• Sketch the line given by the corresponding
  equation (solid if or , dashed if lt or gt).
  This line separates the coordinate plane into 2
  half-planes. In one half-plane all of
  the points are solutions of the inequality.
  In the other half-plane - no point is a
  solution
• You can decide whether the points in an entire
  half-plane satisfy the inequality by testing ONE
  point in the half-plane.
• Shade the half-plane that has the solutions to
  the inequality.

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The graph of an inequality is the graph of all
the solutions of the inequality

• 3x 2y 2
• y -3/2x 1 (put into slope intercept to
  graph easier)
• Graph the line that is the boundary of 2 half
  planes
• Before you connect the dots check to see if the
  line should be solid or dashed
• solid if or
• dashed if lt or gt

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y -3/2x 1
Step 1 graph the boundary
(the line is solid )
Step 2 test a point NOT On the line (0,0) is
always The easiest if its Not on the line!!
3(0) 2(0) 2 0 2 Not a solution
So shade the other side of the line!!
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Graph y lt 6
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4x 2y lt 7
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Assignment