Question

The coordinate plane below represents a city. Points A through F are schools in the city.

Part A: Using the graph above, create a system of inequalities that only contains points C 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 C and F are solutions to the system of inequalities created in Part A. (3 points)

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend. (2 points)

Answer 1

PART A

Refer to the diagram below for the region that only has point C and F inside the shaded region

The three inequalities can be:
y ≥ 1
x ≥ 1
y ≤ -x + 8
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PART B

Coordinate of C is (2, 2)
Coordinate of F is (3, 4)

For the inequality y ≥ 1, the y-coordinate of both point C and F are more than 1

For the inequality x ≥ 1, the x-coordinate of both point C and F are more than 1

For the inequality y ≤ -x + 8
Start with point C, we substitute the x-coordinate = 2 and check whether -x + 8 is indeed more than y
-x + 8 = -(2) + 8 = 6 and 6 ≥ 2

Point D (3, 4), substituting x = 3
-x + 8 = -(3) + 8 = 5 and 5 ≥ 4

So point C and F are solutions to the inequalities
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PART C

Refer to the second diagram below, the points below the line -2x + 2 are A., B, and D. We choose the point below the line because the inequality want 'y' to be less than -2x + 2