Based on the graph you provided, it appears to represent a triangular region bounded by a line with a downward slope. The inequality for the graph can be written by analyzing the boundaries and constraints of the shaded area.

1. Identifying the line: The line has a negative slope, crossing the y-axis at (0, 4) and x-axis at (4, 0).

2. Inequality for the line: The equation of the line can be written as $y = -x + 4$. Since the region is below this line, the inequality is: $y \leq -x + 4$

3. Boundaries for the x and y values: Since the shaded area is bounded between the points $(-4, -4)$ to $(0, 4)$ along the x-axis and above the x-axis, we can express the constraints:

   • $x$ is between $-4$ and $0$: $-4 \leq x \leq 0$
   • $y$ is between the x-axis and the line: $y \geq -4$ and $y \leq -x + 4$

Thus, the full inequality for the graph is: $-4 \leq x \leq 0, \quad -4 \leq y \leq -x + 4$

Would you like further details on the analysis of the graph? Here are some related questions for you:

1. How would the inequality change if the graph had been shifted up or down?
2. How can we graph this inequality step-by-step?
3. What are the properties of linear inequalities like this one?
4. How would the inequality change if the shaded region was above the line instead of below?
5. How do you find the intersection points of linear inequalities?

Tip: When graphing inequalities, always check the direction of the inequality to determine whether the region lies above or below the line!