Background:

You are the financial manager of a furniture company. It is your job to create supply and demand graphs that show the break-even point for the company. The functions that describe how the company can break even will be represented with linear equations. Linear inequalities will be used to graph conditions where the company experiences losses and also where the company would be making a profit.

Before you get started with the actual financial numbers, you will want to practice by creating and comparing various kinds of graphs. To start, you will be comparing the graphs of linear equations with those of linear inequalities.

Task

Consider first a linear equation of the form y = mx + b.

1. Choose values of m and b, then plot the initial equation.

2. Change m to make a different plot.

3. Change b (but not m) in the original equation and plot the result.

4. Finally, use the new values of m and b to create a plot. Place all four on the same graph.

Now choose a linear inequality of the form y < mx + b or y > mx + b.

1. Choose values of m and b, then plot the initial equation.

2. Change m to make a different plot.

3. Change b (but not m) in the original equation, and plot the result.

4. Use the new values of m and b to create a plot.

5. Place all four on the same second graph.

Write a summary that compares the plots on the first graph to one another, then the plots on the second graph to one another, and finally the plots on the first graph to the plots on the second graph. Discuss the effects of changing m, b, and the equality or inequality sign.