Answer: Graph X
Explanation:
First, let's see which graphs have the lines graphed correctly.
W cannot be the correct graph since y = 2x + 1 is graphed wrong. Its y-intercept is supposed to be (0,1).
Y cannot be the correct graph either since y = 2x + 1 is also graphed wrong. The red line on graph Y has a negative slope, which should be positive.
That leaves us with graph X and Z.
We can find the correct graph by selecting a point from the blue region and plugging that point into both of the inequalities. If both inequalities are true when the point is plugged in, there's your answer.
For graph X, let's choose (1,-3).
y ≤ 2x + 1
-3 ≤ 2(1) + 1
-3 ≤ 2 + 1
-3 ≤ 3
-3 is less than or equal to 3. This is true.
y < -x - 1
-3 < -1 - 1
-3 < -2
-3 is less than -2. This is true. Since both inequalities are true, the answer is graph X.
I'm just going to do graph Z to prove that it is not graph Z. Let's choose (0,0) as the point.
y ≤ 2x + 1
0 ≤ 2(0) + 1
0 ≤ 0 + 1
0 ≤ 1
0 is less than or equal to 1. This is true.
y < -x - 1
0 < -0 - 1
0 < -1
0 is less than -1. This is not true. Graph Z is false.