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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Graphing Inequalities in Two Variables

The solution set for an inequality in two variables contains ordered pairs whose graphs fill an area on the coordinate plane called a half-plane. An equation defines the boundary or edge of the half-plane.

 Graphing Inequalities in Two Variables Find the boundary by graphing the equation related to the inequality. If the inequality symbol is < or >, draw the boundary as a dashed line. If the inequality symbol is or , draw the boundary as a solid line to show that the points on the boundary are included in the solution set. Determine which of the two half-planes contains the solutions by choosing a point in each half-plane and testing its coordinates in the inequality. If the coordinates make the inequality true, shade that half-plane.

Example

Graph y - 2 x 1.

Solution

Solve the inequality for y: y - 2x 1. Then, graph the related equation y = 2x + 1. Draw the line as a solid line since the inequality symbol is less than or equal to. Select a point in each of the half-planes and test it in the inequality.

 Test (0, 0) Test (-1, 1) y - 2x 1 y - 2x 1 0 - 2(0) 1 1 - 2(-1) 1 0 1 True 3 1 False

Therefore, the half-plane that contains the point (0, 0) should be shaded.