https://file.aiquickdraw.com/mathbot/file/1726688050221e6xd95j3.jpg

To determine which inequality is shown in the graph, let's first analyze the elements of the image:

1. **Line equation**: 
   - The red line passes through the points (-2, 2) and (0, -2). 
   - The slope (\(m\)) of the line is calculated as the change in \(y\) divided by the change in \(x\):
     \[
     m = \frac{-2 - 2}{0 - (-2)} = \frac{-4}{2} = -2
     \]
   - So, the slope is \(-2\), and using the point \((0, -2)\), we can determine the y-intercept, which is \(-2\). 
   - Therefore, the equation of the line is: 
     \[
     y = -2x - 2
     \]

2. **Shading**: 
   - The graph shows the area above the red line shaded, which means the inequality is \(y \geq -2x - 2\).

Thus, the inequality represented by the graph is:
- **A. \(y \geq -2x - 2\)**

Would you like more details or clarifications?

Here are 5 related questions to expand on this concept:
1. How do you determine the slope of a line from two points?
2. What is the difference between solid and dashed lines in inequality graphs?
3. How do you know whether to shade above or below the line?
4. Can a linear inequality have multiple solutions? Why or why not?
5. What does the y-intercept represent in a graph?

**Tip:** Always remember that the inequality sign (\(\geq\) or \(\leq\)) determines where to shade on the graph: above for \(\geq\) and below

Learn how to solve and interpret the inequality represented in a graph. This problem explores linear equations, slope, y-intercept, and graphing inequalities with shaded regions. Suitable for students in Grades 8-10.

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