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: $3x - 2y \leq 6$