https://file.aiquickdraw.com/mathbot/file/1729414662511xfcvifs2.jpg

To find the equation of the line shown in the image, we need to follow these steps:

1. **Identify two points on the line**: Based on the graph, we can see two clear points:
   - Point 1: \((-6, 4)\)
   - Point 2: \((2, -4)\)

2. **Find the slope (m)**: The slope of a line is calculated by the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Using the points \((-6, 4)\) and \((2, -4)\):
   \[
   m = \frac{-4 - 4}{2 - (-6)} = \frac{-8}{8} = -1
   \]

3. **Use the point-slope form**: The equation of a line in point-slope form is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using one of the points, say \((-6, 4)\), and the slope \(m = -1\):
   \[
   y - 4 = -1(x - (-6))
   \]
   Simplifying:
   \[
   y - 4 = -1(x + 6)
   \]
   \[
   y - 4 = -x - 6
   \]
   \[
   y = -x - 2
   \]

Thus, the equation of the line is:
\[
y = -x - 2
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you find the slope if the line is horizontal or vertical?
2. What is the significance of the slope being negative in this case?
3. Can you rewrite the equation of the line in standard form?
4. How do you find the equation if you are only given the slope and one point?
5. What is the intercept of the line with the y-axis in this equation?

**Tip**: Remember, when finding the slope between two points, always subtract the \(y\)-coordinates first and then the \(x\)-coordinates to avoid mistakes.

Write an equation of the line below based on the graph.

Learn how to find the equation of a line by calculating the slope from two points on a graph and applying the point-slope form. This example uses points (-6, 4) and (2, -4) to derive the equation y = -x - 2.

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