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: erica wants to live in the area defined by y < 7x − 4. explain how you can identify the houses in which erica is interested in living. (2 points)

Part A. The technique on how to find the equation that only applies to point C and F, is to create a line or curve that only includes two of these points. In this case, I created a random line that isolates points C and F from the rest of the points. First, we have to find the equation of the line by choosing at least two points on the line. Using the slope-intercept form: y = mx + b, where m is the slope, Δy/Δx and b is the y-intercept. Let's choose the red points: Point 1(3,3) and Point 2(-4,-4).

m = (-4 - 3)/(-4 - 3) = 1

Then, from the graph, we can see that the intercept is 0. So, the equation of the line is y=x. Now, let's find the inequality symbol that applies to C(2,1) and F(3,-4).

Point C;
y ? x
1 ? 2
1 < 2

Point F:
y ? x
-4 ? 3
-4 < 3

That means the inequality symbol should be <. The complete equation is then y<x.

Part B. The verification is already shown above.

Part C. For y < 7x − 4, ignore the equality symbol first and graph the line. Assign random values of x, then you get corresponding values of y. Plot them as shown in the second picture. The line is shown in red. Next, test the equation by choosing a random point. Let's choose the purple point at (4,3).

3 ? 7(4) − 4
3 ? 24
3 < 24

Thus, it applies to the purple point, and all the other areas to that area. The shaded region are all solutions of the inequality. So, Erica is only interested in points E, C and F.