https://file.aiquickdraw.com/mathbot/file/17265024872249w45f0i2.jpg

The question asks which points represent the solution(s) for the line graphed, and we are given three points to check against the line on the graph.

### The points provided are:
- I: (-2, 0)
- II: (0, -2)
- III: (2, -6)

### Steps to determine the solution:
1. **Verify if each point lies on the line** by checking if the point satisfies the equation of the line. 
   - From the graph, the line seems to have a slope of \( m = -2 \) and passes through the y-intercept at \( (0, -2) \).
   - The slope-intercept form of the line equation is:
     \[
     y = -2x - 2
     \]

2. **Check each point**:
   - For **Point I** (-2, 0): 
     \[
     y = -2(-2) - 2 = 4 - 2 = 2
     \]
     The actual y-coordinate of point I is 0, so this point is **not on the line**.
   
   - For **Point II** (0, -2):
     \[
     y = -2(0) - 2 = -2
     \]
     This matches the y-coordinate of point II, so this point **is on the line**.
   
   - For **Point III** (2, -6):
     \[
     y = -2(2) - 2 = -4 - 2 = -6
     \]
     This matches the y-coordinate of point III, so this point **is on the line**.

### Conclusion:
Points II and III are the solutions for the line graphed. Therefore, the correct answer is:
\[
\boxed{\text{II and III}}
\]

Would you like more details or have any further questions?

### 5 Related Questions:
1. How do you derive the equation of a line from its graph?
2. What is the significance of the slope in the slope-intercept form of a line?
3. How can you verify if a point lies on a given line algebraically?
4. What happens if two points lie on the same line? How does that affect the equation?
5. How do you graph a line using only the slope and y-intercept?

**Tip:** Always ensure the slope and y-intercept are identified correctly from a graph before finding the equation.

Which point(s) represent(s) the solution(s) for the line graphed?

Determine which points lie on the line graphed by using the slope-intercept equation of the line and verifying each coordinate pair. Points (-2, 0), (0, -2), and (2, -6) are checked against the line equation y = -2x - 2. Suitable for students in Grades 8-10.

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