https://file.aiquickdraw.com/mathbot/file/1726257146957njxr6qpb.jpg

To identify which inequality matches the graph, let’s first analyze the graph in detail:

### Graph Description:
- The graph shows a region that is shaded below a diagonal line with a positive slope.
- The line passes through the origin (0,0) and has a positive slope, likely 1, since the line crosses through points like (1,1), (2,2), etc.
- The shading is below this line, which means the inequality will involve either "<" or "≤".
- The line is solid, which suggests the inequality includes "≤" rather than just "<".

### Step-by-Step Matching Process:
We know the general form of the line equation based on its slope:
- The line equation appears to be \( y = x \).

Since the shading is below the line, the inequality is \( y \leq x \).

Now, let’s find the corresponding inequality from the list:

### The correct match is:
- **\( y \leq x \)**, which corresponds to option **(h)**.

### Summary:
The graph matches inequality **(h)**: \( y \leq x \).

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Would you like further explanation on how I analyzed the graph? Here are a few related questions you might find helpful:

1. How do we determine if an inequality is strict or non-strict from a graph?
2. What is the difference between shading above or below a line in graphing inequalities?
3. How can we determine the equation of a line from a graph?
4. What are the steps to graph a linear inequality?
5. How do we convert inequalities to slope-intercept form?

**Tip**: Always check whether the line in a graph is solid or dashed. A solid line means "inclusive" (≤ or ≥), and a dashed line means "exclusive" (< or >).

Learn how to match a graph with its inequality, focusing on the linear equation y ≤ x. The problem involves graphing inequalities and identifying shaded regions, suitable for students in Grades 8-10.

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