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The coordinate plane below represents a town. Points A through F are farms in the town.

graph of coordinate plane. Point A is at 2, negative 3. Point B is at negative 3, negative 4. Point C is at negative 4, 2. Point D is at 2, 4. Point E is at 3, 1. Point F is at negative 2, 3.

Part A: Using the graph above, create a system of inequalities that only contains points D and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)

Part B: Explain how to verify that the points D and F are solutions to the system of inequalities created in Part A. (3 points)

Part C: Chickens can only be raised in the area defined by y > 2x − 2. Explain how you can identify farms in which chickens can be raised. (2 points)

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  1. A: The line through D and F is
    y = x/4 + 7/2
    So, since all the other points lie below this line, and above C, you need

    2 < y < x/4 + 7/2

    C: Just plug in the points and see whether they satisfy y > 2x-2

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