Question

1. write the system of inequalities that is graphed.

Explanation:

Step1: Identify horizontal boundary

The shaded region is above the horizontal line $y=7$, and the line is solid, so the inequality is $y \geq 7$.

Step2: Find line equation for slant line

Use two points on the line: $(-6,1)$ and $(0,4)$. Calculate slope:
$\text{slope } m = \frac{4-1}{0-(-6)} = \frac{3}{6} = \frac{1}{2}$
The y-intercept $b=4$, so the line equation is $y = \frac{1}{2}x + 4$.

Step3: Determine slant line inequality

The shaded region is above the solid slant line, so the inequality is $y \geq \frac{1}{2}x + 4$.

Answer:

$$\begin{cases} y \geq 7 \\ y \geq \frac{1}{2}x + 4 \end{cases}$$