Questions: y ≤ x-2 y ≥ 1/4 x-4

Solution Steps

The first inequality is $y \le x - 2$. The corresponding line is $y = x - 2$, which has a y-intercept of -2 and a slope of 1. The inequality states that $y$ is less than or equal to $x-2$, so the region below the line $y = x - 2$ (including the line itself) satisfies this inequality.

The second inequality is $y \ge \frac{1}{4}x - 4$. The corresponding line is $y = \frac{1}{4}x - 4$, which has a y-intercept of -4 and a slope of 1/4. The inequality indicates that $y$ is greater than or equal to $\frac{1}{4}x - 4$, so the region above the line $y = \frac{1}{4}x - 4$ (including the line itself) satisfies this inequality.

The solution region is the intersection of the regions described in steps 1 and 2. Looking at the graph, this corresponds to Region B.

Final Answer: The correct answer is C. Region B.