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### Problem:
Find the equation of the line passing through the points (-3, 7) and (2, -6).

1. **Find the slope of the line:**
   The slope formula 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 \((-3, 7)\) and \((2, -6)\):
   \[
   m = \frac{-6 - 7}{2 - (-3)} = \frac{-6 - 7}{2 + 3} = \frac{-13}{5}
   \]
   So, the slope \(m = \frac{-13}{5}\).

2. **Point-slope form:**
   The point-slope form of a line is given by:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using the point \((-3, 7)\) and the slope \(m = \frac{-13}{5}\):
   \[
   y - 7 = \frac{-13}{5}(x - (-3)) = \frac{-13}{5}(x + 3)
   \]
   This is the equation in point-slope form.

3. **Slope-intercept form:**
   To convert the equation to slope-intercept form (\(y = mx + b\)), we can simplify:
   \[
   y - 7 = \frac{-13}{5}(x + 3)
   \]
   Expanding the right side:
   \[
   y - 7 = \frac{-13}{5}x - \frac{39}{5}
   \]
   Adding 7 to both sides (which is equivalent to \(\frac{35}{5}\)):
   \[
   y = \frac{-13}{5}x - \frac{39}{5} + \frac{35}{5} = \frac{-13}{5}x - \frac{4}{5}
   \]
   So, the slope-intercept form is:
   \[
   y = \frac{-13}{5}x - \frac{4}{5}
   \]

---

**Summary of the answers:**
- (a) The slope is \(\frac{-13}{5}\).
- (b) The point-slope form is \(y - 7 = \frac{-13}{5}(x + 3)\).
- (c) The slope-intercept form is \(y = \frac{-13}{5}x - \frac{4}{5}\).

Would you like further clarification or details on any part?

### Follow-up questions:
1. How is the point-slope form of a line derived?
2. What are the key differences between point-slope form and slope-intercept form?
3. Can a line passing through two points ever have an undefined slope?
4. How can you verify the equation of a line given two points?
5. What happens if two points have the same \(x\)-coordinate?

### Tip:
Always double-check your calculations for the slope, as a small mistake can change the entire equation of the line!

Find the equation of the line passing through the points (-3, 7) and (2, -6).

Learn how to find the equation of a line passing through the points (-3, 7) and (2, -6). This problem involves finding the slope and writing the equation in both point-slope and slope-intercept forms. Suitable for students in Grades 9-12.

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