https://file.aiquickdraw.com/mathbot/file/172936174034762jc05ch.jpg

The graph shows a straight line, and the task is to find the equation of the line.

### Steps to find the equation of the line:

1. **Identify two points on the line:**  
   From the graph, two clear points where the line passes through are:
   - Point 1: \((-3, -4)\)
   - Point 2: \((3, 2)\)

2. **Find the slope \( m \):**  
   The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the points \((-3, -4)\) and \((3, 2)\):
   \[
   m = \frac{2 - (-4)}{3 - (-3)} = \frac{2 + 4}{3 + 3} = \frac{6}{6} = 1
   \]

3. **Find the y-intercept \( b \):**  
   Using the slope-intercept form of a line, \( y = mx + b \), we substitute the slope \( m = 1 \) and use one of the points, say \((3, 2)\), to solve for \( b \):
   \[
   2 = 1(3) + b \implies 2 = 3 + b \implies b = 2 - 3 = -1
   \]

4. **Write the equation:**  
   Now that we know the slope \( m = 1 \) and the y-intercept \( b = -1 \), the equation of the line is:
   \[
   y = x - 1
   \]

This is the equation that represents the line.

Would you like more details on any part of this solution, or have any questions?

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Here are 5 questions related to this problem:
1. How would the equation change if the slope were negative?
2. What happens to the y-intercept if the line shifts vertically?
3. How would you verify that the points \((-3, -4)\) and \((3, 2)\) lie on the equation \(y = x - 1\)?
4. What is the general form of a linear equation, and how does it differ from the slope-intercept form?
5. How do parallel lines relate in terms of their slopes?

**Tip:** When finding the slope, always subtract the y-coordinates first and then the x-coordinates, to avoid sign errors.

Write an equation that represents the line passing through points (-3, -4) and (3, 2).

Learn how to find the equation of a line passing through the points (-3, -4) and (3, 2). This problem involves calculating the slope and using the slope-intercept form of a linear equation. Suitable for students in Grades 8-10.

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