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The inequality represented by the graph shows a shaded region above a line with a negative slope, and the line itself appears to be solid, indicating that the points on the line are included in the solution. Let's break this down:

1. **Equation of the line**: The line passes through two points, \((-6, 4)\) and \((0, 2)\). Using the slope formula:
   \[
   \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 4}{0 - (-6)} = \frac{-2}{6} = -\frac{1}{3}
   \]
   So, the slope is \(-\frac{1}{3}\).

   Using the slope-intercept form \(y = mx + b\), we already know the slope \(m = -\frac{1}{3}\) and the y-intercept \(b = 2\) (since the line crosses the y-axis at \((0, 2)\)).

   Therefore, the equation of the line is:
   \[
   y = -\frac{1}{3}x + 2
   \]

2. **Shading and inequality**: The region above the line is shaded. This suggests that the inequality involves greater than or equal to (\(\geq\)) because the points on the line are included (solid line), and the shading is above the line.

   So, the inequality is:
   \[
   y \geq -\frac{1}{3}x + 2
   \]

3. **Answer selection**: The correct inequality corresponds to option **D**:
   \[
   y \geq -\frac{1}{3}x + 2
   \]

Would you like further details or have any questions?

Here are some related questions for further practice:
1. How do you determine the slope of a line from a graph?
2. How does the shading in an inequality graph affect the inequality symbol?
3. What does the solid line in a graph of an inequality represent?
4. How would the inequality change if the region below the line were shaded instead?
5. How do you convert between the equation of a line and its graph?

**Tip**: When graphing inequalities, always pay attention to whether the line is solid (includes the boundary) or dashed (excludes the boundary).

Learn how to interpret a graph showing a linear inequality. This problem focuses on finding the equation of a line, calculating its slope, and understanding shaded regions representing inequalities. Suitable for students in Grades 8-10.

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