1. Graph and solve systems of linear inequalitites A-CED 3

2. Review graphing linear equations Slope-Intercept form 1. Plot a point on the y-axis (y-intercept) 2.Plot the second point by counting the rise and run (slope) from the y-intercept point.

3. Review graphing linear equations Standard Form 1. Put in slope-intercept form (solve for y).

4. Review graphing linear equations Vertical Line Horizontal Line

5. What does a graph represent?  Graphs represent solutions of the equation.

6. If I wanted to graph an inequality, how would I represent all possible ordered pairs that are solutions to the problem? SSHADE

7. Graphing Inequalities Graph the line using y-intercept and slope Since the problem is an inequality, we need to shade one side of the line to represent all the possible solutions to the inequality.

8. If the shaded region represents the solutions to the inequality, how can I check my answer? Pick a point and substitute in the inequality to see if the statement is true.

9. Graphing Inequalities I pick the origin (0,0) Therefore the shading is correct.

10. Graphing Inequalities I pick the origin (0,0) Shade the side of the line containing the origin.

11. Graphing Inequalities NOTE: You can not pick a point that lines on the line. I pick the point (-1,3) Shade the side opposite the point you picked.

12. Graphing Inequalities

16. Linear Programming  Your club plans to raise money by selling two sizes of fruit baskets. The plan is to buy small baskets for $10 and sell them for $15 and buy large baskets for $15 and sell them for $24. The club president estimates that you will not sell more than 100 baskets. Your club can afford to spend up to $1200 to buy baskets. Find the number of small and large baskets you should buy in order to maximize profit.

17. 0 20 40 60 Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets Total baskets constraint Total spending constraint baskets minimum constraint 80 10 0 20406080 10 0 Feasibility region vertices

18. 0 20 40 60 Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets 80 10 0 20406080 10 0 Feasibility region (0, 80) (60, 40) (0, 0) (100, 0) vertices

19. Objective Function: 5x + 9y (maximum profit) x = # of small baskets y = # of large baskets (0, 80) (60, 40) (0, 0) (100, 0) minimum maximum Check for maximum profit by plugging each vertice of the feasibility region into the objective function.