Nov. 13 Linear Inequalities
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Nov. 13 Linear Inequalities

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Nov. 13 Linear Inequalities Nov. 13 Linear Inequalities Document Transcript

  • Linear Inequalities 1
  • A linear inequality has a boundary line that can be  expressed in the form y = mx + b The solution to the inequality is the set of all ordered pairs  that makes the inequality true. 2
  • Example Graph 2x + y < 4 3
  • 1. Graph inequality like a linear equation.  2. Line becomes boundary line. ­ if > (greater than) boundary line is dashed  because values are not  ­ if < (less than)  part of solution ­ if          (greater than or equal to) boundary line is  solid because values  ­ if          (less than or equal to) are part of solution 4
  • 3. Test a point on each side of the boundary line to determine      the solution area.  4. Shade in the region that represents the solution. 5
  • Example Graph y ­ 3 ≥ 0 6
  • Graph the solution of  4x ­ y ≤ 6 7
  • System of linear inequalities:  Two types of systems. 1. Intersection of the inequalities   ( and ) and The solution to the system is where the solutions for  each individual inequality overlap 2. Union of the inequalities     ( or ) or The solution to the system could be anywhere  within either solution set of each inequality.... combine their solution sets 8
  • and 9
  • or 10
  • Exercise 27 Questions 1 ­ 11 11