Looking at the graph, the blue shaded area represents the solution set to a linear inequality. The boundary line is drawn as $2x + y = 6$, and the shading appears below the line, indicating that the inequality is either $2x + y \leq 6$ or $2x + y < 6$.

Since the boundary line is solid, the inequality includes the boundary, so the correct inequality is:

$2x + y \leq 6$

Would you like further details or explanation about this solution?

Here are 5 related questions to deepen understanding:

1. How can you determine whether to use $\leq$ or $<$ in an inequality?
2. What would the solution look like if the inequality was $2x + y > 6$?
3. How would the inequality change if the shading were above the line?
4. Can this inequality be rewritten in a different form (e.g., slope-intercept form)?
5. How do you find the slope of the line from the inequality $2x + y = 6$?

Tip: When interpreting shaded areas in graphs, always check if the boundary line is solid (indicating $\leq$ or $\geq$) or dashed (indicating $<$ or $>$).