https://file.aiquickdraw.com/mathbot/file/1729178070928akq38dfq.jpg

To identify the inequality represented by the shaded region on the graph, let's analyze the line and shading pattern.

### Step 1: Determine the equation of the boundary line
1. The boundary line appears to go through the points \((-3, 0)\) and \((0, 3)\).
2. To find the slope (\(m\)) of the line:
   \[
   m = \frac{3 - 0}{0 - (-3)} = \frac{3}{3} = 1
   \]
   The slope is \(1\).
3. Using the point-slope form, we can express the equation of the line:
   \[
   y - 3 = 1(x - 0) \implies y = x + 3
   \]

### Step 2: Convert the equation to the form in the options
To match it with the forms provided in the multiple-choice options, rearrange:
\[
y - x \leq 3
\]

Now, let's rewrite this as:
\[
x - y \geq -3
\]

### Step 3: Identify the correct inequality
The shading is above the line, which means it includes points where \(y\) is greater than the line (\(x + 3\)). This corresponds to:
\[
x - y \geq -3
\]

To match the options, this is equivalent to:
\[
3x - 2y \leq 6
\]



Learn how to identify which linear inequality corresponds to a shaded region on a graph. This problem focuses on analyzing slope, boundary lines, and inequality signs. Suitable for students in Grades 8-10.

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