The coordinate plane below represents a town. Points A through F are farms in the town. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at 1, negative 2. Point E is at 5, negative 4. Point F is at 3, 4. Part A: Using the graph above, create a system of inequalities that only contains points A 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 A 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 < −2x + 4. Explain how you can identify farms in which chickens can be raised. (2 points)
Accepted Solution
A:
we have that A (-3,-4) B (-4,3) C (2,2) D (1,-2) E (5,-4) using a graph tool see the attached figure N 1
Part A: Using the graph above, create a system of inequalities that only contains points A and E in the overlapping shaded regions.
A (-3,-4) E (5,-4) y<= -3 y>=-5 is a system of a inequalities that will only contain A and E to graph it, I draw the constant y = -3 and y=-5 and and I shade the region between both lines see the attached figure N 2
Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A
we know that the system of a inequalities is y<= -3 y>=-5 the solution is all y real numbers belonging to the interval [-5,-3]
therefore if points A and E are solutions both points must belong to the interval
points A and E have the same coordinate y=-4 and y=-4 is included in the interval
therefore both points are solution
Part C: Chickens can only be raised in the area defined by y < −2x + 4. Explain how you can identify farms in which chickens can be raised
step 1 graph the inequality y < −2x + 4 see the attached figure N 3 the farms in which chickens can be raised are the points A, B and D are those that are included in the shaded part