Question

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

graph of coordinate plane. Point A is at 1, 3. Point B is at 3, 1. Point C is at 3, negative 3. Point D is at negative 4, 2. Point E is at negative 1, 5. Point F is at negative 3, negative 3.

Part A: Using the graph above, create a system of inequalities that only contains points D and E 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 E 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 > 3x − 4. Explain how you can identify farms in which chickens can be raised. (2 points)

Answer 1

To solve this, use the point - slope form formula
Point D (-4, 2) and Point E (-1, 5)
y - y1 = [(y2 - y1)/(x2 - x1)](x - x1)
y - 2 = [(5 - 2/-1 -(-4))](x + 4)
y - 2 = x + 4
y = x + 6

To answer this, input the values of points D or E into the equation and make sure that they answer the equation in part A.
y = x + 6
2 = -4 + 6 = -2 so it satisfies the solution