https://file.aiquickdraw.com/mathbot/file/1728043492333otyqpajh.jpg

The image shows a graph with a line passing through different points, and the task is to determine which of the listed points represents the solution(s) for the line graphed. The points provided are:

- Point I: (-2, 0)
- Point II: (0, -2)
- Point III: (2, -6)

To solve this, we can first observe the equation of the line visually or by checking which points lie directly on the line.

### Step-by-Step Analysis:

1. **Point I: (-2, 0)**  
   Looking at the graph, point (-2, 0) lies on the x-axis where the line crosses, so **Point I is a solution**.

2. **Point II: (0, -2)**  
   Point (0, -2) represents the y-intercept, where the line crosses the y-axis. This point is clearly on the line, so **Point II is also a solution**.

3. **Point III: (2, -6)**  
   Finally, checking point (2, -6), this point appears to lie on the line as well. So, **Point III is also a solution**.

### Conclusion:
The points that represent solutions for the line are **I, II, and III**. Therefore, the correct answer is:

- **Option D: I and III**

Would you like any details or further clarification on the process?

### Follow-up Questions:
1. How do we determine the equation of a line based on a graph?
2. Can all lines be expressed as a linear equation?
3. What is the significance of the slope in determining solutions to lines?
4. How do we calculate the slope using two points?
5. How can you verify graphically whether a point lies on a line?

### Tip:
When checking if a point lies on a line, you can plug the coordinates into the line's equation to see if the equation holds true!

Which point(s) represent the solution(s) for the line graphed? Points: I (-2, 0), II (0, -2), III (2, -6).

Determine which points represent the solutions for a graphed line. This problem covers graphing and linear equations, testing points (-2, 0), (0, -2), and (2, -6) to see if they lie on the line.

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