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The graph provided shows a red line passing through the points \((-2, 2)\) and \((0, -2)\). The shaded region is below the line. The goal is to find the inequality that represents this situation.

### Step-by-step solution:

1. **Find the equation of the line:**
   - The slope (\(m\)) of the line can be found using the slope formula:
     \[
     m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 2}{0 - (-2)} = \frac{-4}{2} = -2
     \]
   - The slope is \(m = -2\).
   
   Using the point-slope form of a line \(y = mx + b\), we can substitute the slope and one of the points, say \((0, -2)\), to find the y-intercept \(b\):
   \[
   -2 = -2(0) + b \implies b = -2
   \]
   
   Therefore, the equation of the line is:
   \[
   y = -2x - 2
   \]

2. **Determine the inequality:**
   - Since the shaded region is below the line, this means the inequality should be \(y \leq -2x - 2\) (because the area below a line means \(y\) is less than or equal to the line's equation).

3. **Conclusion:**
   The correct inequality that represents the shaded region in the graph is:
   \[
   \boxed{y \leq -2x - 2}
   \]
   Therefore, the answer is **Option A**.

Would you like further clarification or details on any step?

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Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. What does the slope represent in an equation of a line?
3. How do you know whether the inequality sign should be \(\leq\) or \(\geq\)?
4. What is the point-slope form of a linear equation?
5. How do you graph an inequality in two variables?

**Tip:** When graphing inequalities, always remember that the shaded area represents the solution set where the inequality holds true.

Learn how to identify linear inequalities from a graph. This example demonstrates the inequality y ≤ -2x - 2 by analyzing the slope and shaded region. Suitable for Grades 7-9.

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