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Graphing Inequalities in Two Variables

This topic covers the concept of graphing inequalities on a coordinate plane along with some word problems.

Topic: Graphing Inequalities

  • A graph of a linear equation separates the coordinate plane into three parts: the points on one side of the line, the points on the boundary line, and the points on the other side of the line

  • To graph an inequality, first graph the boundary line; for example to plot
    y < x + 3, first plot the boundary line y = x + 3

  • Dashed line shows that the points on the line are not included in the solution set

  • Solid line shows that the points on the line are included in the solution set

  • To determine on which side of the line the solution lies, test a point which does not lie on the line and then shade the area accordingly

Topic: Word Problems

  • A graph of a linear equation separates the coordinate plane into three parts: the points on one side of the line, the points on the boundary line, and the points on the other side of the line

  • To graph an inequality, first graph the boundary line; for example to plot
    y < x + 3, first plot the boundary line y = x + 3

  • Dashed line shows that the points on the line are not included in the solution set

  • Solid line shows that the points on the line are included in the solution set

  • To determine on which side of the line the solution lies, test a point which does not lie on the line and then shade the area accordingly
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