Question

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 − 5. Explain how you can identify the houses in which John is interested in living. (2 points)

Answer 1

I color coded everything so you can explain in your own words what I did. Everything is labeled.
Part A. Used the points to find the lines I needed using slope formula and formed the y=mx+b form of the line. Then I used the inequality that helped me to include only B and F.
Part B. Used my inequalities and used points B and F to see if the inequalities were true. If true then they work as solutions, if false then they do not. Yours are true, they are solutions.
Part C. Drew the line in green so you could see it and verify the houses. You could also use the line equation and plug in every point house letter and if they are true they are a house John is interested in, if false then that house he is not interested in. I used graphing the line to show you better how to solve.