Question

y = \frac{1}{4}x + 3; y > -4x - 1

Explanation:

Step1: Verify first inequality line

The line for $y = \frac{1}{4}x + 5$ has a y-intercept of 5 and slope $\frac{1}{4}$. The inequality $y \geq \frac{1}{4}x + 5$ means we shade above this solid line (since $\geq$ uses a solid line).

Step2: Verify second inequality line

The line for $y = -4x - 1$ has a y-intercept of -1 and slope $-4$. The inequality $y > -4x - 1$ means we shade above this dashed line (since $>$ uses a dashed line).

Step3: Identify overlapping shaded region

The solution is the area that satisfies both inequalities: above the solid line $y = \frac{1}{4}x + 5$ and above the dashed line $y = -4x - 1$, which matches the shaded region in the graph.

Answer:

The shaded region in the graph correctly represents the solution set of the system of inequalities $\boldsymbol{y \geq \frac{1}{4}x + 5}$ and $\boldsymbol{y > -4x - 1}$.