Finite Math Mrs. Piekos

 Move from equation to inequalities ◦ ax + by + c = 0 ◦ ax + by + c ≤ 0, ax + by + c ≥ 0, ax + by + c 0  Review the Shaded regions – what is or is not included with the system  Procedure for graphing inequalities  Define Bounded and Unbounded Solution Sets  Questions you will be asked to apply ◦ Graph the solution for the inequality ◦ Write a system of linear inequalities ◦ Determine the graphical solution set for each system, determine if bounded or unbounded

Graphing Linear Inequalities Ex. Graph Notice that the line (=) is part of the solution Also, any point in the lower half-plane satisfies the inequality so this region is shaded. x y

Graphing Linear Inequalities Ex. Graph The line (=) is not part of the solution so it is dashed. Any point in the lower half-plane satisfies the inequality. x y

Procedure for Graphing Linear Inequalities 1.Draw the graph of the equation obtained by replacing the inequality symbol with an equal sign. Make the line dashed if the inequality symbol is, otherwise make it solid. 2.Pick a test point in one of the half planes, substitute the x and y values into the inequality (use the origin whenever possible). 3.If the inequality is satisfied, shade the half plane containing the test point otherwise shade the other half plane.

Ex. Graph Dashed since < True so shade region containing (0,0) Test (0,0): 3(0)+2(0) < 6 y x

Ex. Graph x x yy More Graphing Examples

1. 2.

Ex. Graph the solution set for the system: Points must satisfy both inequalities (overlap of individual shaded regions) y x

3. 4.

Bounded Region Unbounded Region x y x y Regions: Bounded and Unbounded