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 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)

Answer 1

we have that
A (2,-3)
B (-3,-4)
C (-4,2)
D (2,4)
E (3,1)
F(-2,3)
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 (2,-3) E (3,1)
y<= 1
x>=2
is a system of a inequalities that will only contain A and E
to graph it, I draw the constant y = 1 and x=2 and the shaded part is below y=1 and to the right of x=2
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<= 1
x>=2
the solution is
domain
all x real numbers belonging to the interval [2,∞)
and
range
all y real numbers belonging to the interval (-∞,1]

therefore
if points A and E are solutions both points must belong to the domain and range interval
point A (2,-3)
2 is included in the interval [2,∞)
-3 is included in the interval (-∞,1]

point E (3,1)
3 is included in the interval [2,∞)
1 is included in the interval (-∞,1]

therefore
both points are solution


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

step 1
graph the inequality y > 2x-2
see the attached figure N 3
the farms in which chickens can be raised are the points B, C, D and F
are those that are included in the shaded part