Step-by-step explanation:
Step 1: Let's evaluate the inequality y ≥ 1/2x -2.
First, since the symbol ≥ is used the extremes are included. So, it has to be a continuous line.
If you obserse the point of the line y = 1/2x - 2:
x = 0; y = 1/2*0 - 2 = -2
(0, -2)
And
x = 2; y = 1/2*2 - 2 = 1 - 2 = -1
(2, -1)
You can observe that it is the line that is "more horizontal".
Since it asked for y-values equal or greater to 1/2x -2, the part at the top of the line must be highlighted.
So, you have options A and C.
Step 2: Let's evaluate the inequality y > -2x - 4
First, since the symbol > is used the extremes are not included. So, it has to be a dropped line.
Second, since y-values greater than -2x - 4 are required, the right part has to be highlighted.
Observing the graphs,
The answer is C.