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To solve this question, we need to use the point-slope form of a linear equation:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \((x_1, y_1)\) is a point on the line (in this case, \((6, -1)\))
- \(m\) is the slope of the line (in this case, \(-\frac{3}{2}\))

### Step-by-step Solution:
1. **Substitute the values**:
   - \(x_1 = 6\), \(y_1 = -1\)
   - \(m = -\frac{3}{2}\)

   Substituting into the point-slope form:

   \[
   y - (-1) = -\frac{3}{2}(x - 6)
   \]

2. **Simplify the equation**:
   - The left-hand side becomes \(y + 1\):
   
   \[
   y + 1 = -\frac{3}{2}(x - 6)
   \]

3. **Distribute the slope**:
   
   \[
   y + 1 = -\frac{3}{2}x + 9
   \]

4. **Isolate \(y\)**:
   Subtract 1 from both sides:

   \[
   y = -\frac{3}{2}x + 8
   \]

### Final Equation:
The equation of the line is:

\[
y = -\frac{3}{2}x + 8
\]

You can now submit this equation.

Do you want more details or have any questions about the solution?

Here are some related questions to expand your understanding:
1. How do you convert a point-slope form equation to slope-intercept form?
2. What happens to the equation if the slope changes to \(\frac{3}{2}\)?
3. How do you find the slope of a line given two points?
4. What is the general form of a linear equation?
5. How do you check if a point lies on a given line?

**Tip**: Always double-check your arithmetic when solving for linear equations.

What is the equation of the line that passes through the point (6, -1) and has a slope of -3/2?

Learn how to find the equation of a line that passes through the point (6, -1) and has a slope of -3/2. This problem involves key concepts like point-slope form and converting to slope-intercept form. Suitable for students in Grades 8-10.

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