Question

y = -1/4 x + 2; y > -4x - 1

Explanation:

Step1: Identify the solid line equation

The solid line has a slope $m=\frac{1}{4}$ (rises 1, runs 4) and y-intercept $b=3$, so its equation is $y=\frac{1}{4}x+3$. The shaded region is above this line, so the inequality is $y\geq\frac{1}{4}x+3$.

Step2: Identify the dashed line equation

The dashed line has a slope $m=-4$ (falls 4, runs 1) and y-intercept $b=-1$, so its equation is $y=-4x-1$. The shaded region is above this line, so the inequality is $y>-4x-1$.

Step3: Combine the inequalities

The system is the two inequalities together.

Answer:

The system of inequalities for the shaded region is:
$y\geq\frac{1}{4}x+3$
$y>-4x-1$