The coordinate plane below represents a community. Points A through F are houses in the community.The coordinate plane⬇︎⬇︎Part A: Using the graph above, create a system of inequalities that only contains points A and B 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 B are solutions to the system of inequalities created in Part A. (3 points)Part C: Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested in living. (2 points)

Accepted Solution

A1) One possible set of inequalities is
  x +y > 2
  y -x < 4

A2) The lines are graphed as though the inequality were an equal sign. Since the inequality does not include the "or equal to" case, the lines are drawn dashed. In each case, the area to the right of the line is shaded.

B) Points A and B are solutions to the system if they are in the doubly-shaded region (which they are). In the graph here, that region is darker orange. (For this purpose, you need to ignore the green region, which overlaps part of the solution space.

C) The houses Billy is interested in are found by graphing the inequality and identifying the houses in its solution space. (Those houses are B and C.) Alternatively, you can evaluate the inequality for each of the house coordinates and see which ones give "true."