Solving Linear Inequalities in Two Variables

This Solving Linear Inequalities in Two Variables presentation also includes:

Although graphing a linear inequality on the plane is but a few steps added onto the graphing of a linear equation, for many learners the logical leap is quite intimidating. This approachable PowerPoint presentation breaks graphing inequalities down into almost algorithmic, easily remembered, steps. Examples of both pure math and applied word problems demonstrate these steps one by one, along with an integrated online graphing tool that allows for class experimentation and adaptation. A strong bridge between graphing equations and inequalities and a great presentation to add to any curriculum inclusive of inequality graphing.

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CCSS: Adaptable
Instructional Ideas

  • Extend by having pupils create problems for one another using current event data. For example, take a total score for a sporting event and graph the possible scores for the two teams
  • Give learners a graph and challenge them to find the generating inequality
  • After graphing an inequality, check for understanding by giving points or contextual information and asking if it is a solution (in the shaded area) or not
Classroom Considerations

  • PowerPoint is saved as a newer file extension (.pptx), which may require additional resources
  • Geogebra example problem interactive solver requires Internet access
  • No explicit treatment of x > 0 or y > 0 boundary conditions, just common sense non-negative answers in physical situations

  • Clear step-by-step walkthrough for the process of graphing a linear inequality
  • PowerPoint presentation is customizable
  • Emphasis on context of word problems not just numeric solutions
  • Interactive solver applet linked to examples, pre-filled with example notation and numbers
  • Keystroke directions for finding solutions of inequaties on TI-83/84/Nspire calculators

  • No example 2 between examples 1 and 3
  • Shading below the line is missing on slide 30