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 contain points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.

Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A.

Part C: William can only attend a school in his designated zone. William's zone is defined by y < -x -1. Explain how you can identify the schools that William is allowed to attend.

Answer 1

PART A: The equation I used is y≥-1x+4. The line will be graphed going diagonally from the second quadrant to the fourth quadrant and shaded above the line.

PART B: Plug in the coordinates for point C and F into the equation from PART A and solve them to make sure the statements are true. You should end up with 2≥2 for point C and 4≥1 for point F.

PART C: First graph the equation and then shade below the line. Next, identify all the points in the shaded area.

I hope this helps you! I have provided pictures of both equations for reference. The first picture is for PART A and PART B. The second picture is for PART C. Let me know if I'm correct :)