https://file.aiquickdraw.com/mathbot/file/1727186990871dgxeh6zo.jpg

To determine the table of values for the green line from the graph, we need to first identify key points along the green line and use them to find a relationship between \(x\) and \(y\).

### Steps:
1. **Identify Key Points**: From the graph, we can see that the green line passes through two specific points:
   - \( (0, -10) \)
   - \( (10, 10) \)

2. **Find the Slope**:
   The slope \(m\) of the line is calculated using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Using the points \( (0, -10) \) and \( (10, 10) \):
   \[
   m = \frac{10 - (-10)}{10 - 0} = \frac{20}{10} = 2
   \]
   So, the slope of the green line is \(2\).

3. **Determine the Equation of the Line**:
   The equation of a line in slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Since the green line passes through the point \( (0, -10) \), the y-intercept \(b = -10\).

   Therefore, the equation of the green line is:
   \[
   y = 2x - 10
   \]

4. **Create the Table of Values**:
   We can now use this equation to calculate \(y\) values for different \(x\) values. Here is the table of values for some selected points:

   | \(x\)  | \(y = 2x - 10\) |
   |-------|-----------------|
   | 0     | \(-10\)         |
   | 2     | \(-6\)          |
   | 4     | \(-2\)          |
   | 6     | 2               |
   | 8     | 6               |
   | 10    | 10              |

Would you like more details on any of these steps or further clarifications?

### Related Questions:
1. How do you determine the slope of a line from a graph?
2. What is the importance of the y-intercept in the equation of a line?
3. How can we verify the correctness of the line equation using points?
4. What would change if the line had a negative slope instead?
5. How can this method be applied to a real-world situation?

### Tip:
When graphing lines, always use at least two clear points to calculate the slope and intercept accurately!

Determine the table of values that represent the green line in the coordinate plane.

Learn how to calculate the table of values for a line on a coordinate plane. Using the slope-intercept form, this guide explains the step-by-step process for finding key points, calculating slope, and creating the table of values. Suitable for Grades 8-10.

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