The coordinate plane below represents a community. Points A through F are houses in the community. graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4. Part A: Using the graph above, create a system of inequalities that only contains points B 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 B and F are solutions to the system of inequalities created in Part A. (3 points) Part C: John wants to live in the area defined by y > 2x βˆ’ 5. Explain how you can identify the houses in which John is interested in living. (2 points)

Accepted Solution

Part A: Points C and F can be isolated by a single line parallel to a line through A and B. Such a line might be the boundary of an inequality such as
Β  7x -9y > -5
If you want two inequalities, you could use
y < 2
x > 0
These will graph as dashed horizontal and vertical lines, with shading below and to the right. The doubly-shaded area will include points C and F.

Part B: One can verify that points C and F are solutions to the system of inequalities either by putting their coordinates into the inequalities, or by consulting the graph.

Part C: You can identify the houses of interest to Erica by graphing the inequality and identifying the points that are in the solution space. In the attached graph, that inequality is graphed in pink. The houses of interest to Erica are shown to be A, C, E, F. Houses B and D are not in the solution space.