https://file.aiquickdraw.com/mathbot/file/1729180261197ybm39x1t.jpg

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.

Which inequality best represents the graph?

Understand how to graph linear inequalities and determine which inequality represents a given graph. This problem involves finding the slope, identifying the shaded region, and understanding inequality symbols. Suitable for Grades 8-10 students.

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