Learning Objective We will learn how to graph Linear Inequalities. We will apply linear inequalities to real-world situations and understand where appropriate constraints apply.

GSE A.REI.12 – Graph the solution set to a linear inequality in two variables.

A company that manufactures MP3 players needs to hire more workers to keep up with an increase in orders. Some workers will be assembling the players and others will be packaging them. The company can hire no more than 15 new employees.

Write a linear inequality that can model this situation. Let x = the number of workers who will assemble the MP3 players. Let y = the number of workers who will package the MP3 players.

① Find the x and y intercepts and graph the function. ② Will the line be dashed or solid? Why? What does this mean about the solutions to the equation?

① Are there constraints for the graph? Why? ② Where would the constraints be?

Where would we shade the graph?

① Test the point (0, 0) in the inequality and see if it makes the inequality true. ② What would this point mean about the word problem? ③ Is all of the shaded region appropriate solutions for the context? ④ Shade the appropriate region.

x & y-intercept What does x-intercept mean in relationship to the context? What does the y-intercept mean in relationship to the context?

Continuous or Discrete? Why? How do we graph this differently? What does this mean? Choose 2 points that are one the line or in the shaded regions. Be prepared to discuss what your points mean in relationship to the context.

Find Missing Points If they hire 7 people to assemble the MP3 players how many people will package them? If they hire 4 people to package the MP3 players how many people will assemble them?