Looking at the graph and the inequality question:

1. Identifying the line equation: The boundary line passes through the point $(0, -1)$, meaning the y-intercept is $-1$. The slope of the line can be found by counting the rise over the run between two points on the line. From $(0, -1)$ to $(2, 0)$, the slope is $\frac{1}{2}$. Thus, the equation of the line is:

   $y = \frac{1}{2}x - 1$

2. Shaded region: The shaded region is below the line, meaning the inequality should use $\leq$ or $<$, since it's the area where $y$ is less than or equal to $\frac{1}{2}x - 1$.

3. Solid line: The line is solid, indicating the inequality includes the line itself, so the inequality will use $\leq$ rather than $<$.

Based on this analysis, the inequality that best represents the graph is:

$\boxed{y \leq \frac{1}{2}x - 1}$

Thus, the correct answer is D.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you calculate the slope of a line?
2. What is the difference between $<$ and $\leq$ in graphing inequalities?
3. How does shading help determine the inequality direction?
4. What is the general form of a linear inequality?
5. How do you convert a linear equation to an inequality?

Tip: To check if a region is correctly shaded, you can test a point (like $(0, 0)$) in the inequality to see if it satisfies the condition.