To solve the equation \( y - 1 = -\frac{3}{2}(x - 4) \) for \( y \), follow these steps:

1. **Distribute** the \(-\frac{3}{2}\) across the \((x - 4)\):
   \[
   y - 1 = -\frac{3}{2}x + \frac{3}{2} \cdot 4
   \]
   \[
   y - 1 = -\frac{3}{2}x + 6
   \]

2. **Add 1** to both sides to solve for \( y \):
   \[
   y = -\frac{3}{2}x + 6 + 1
   \]
   \[
   y = -\frac{3}{2}x + 7
   \]

So, the equation in slope-intercept form is:
\[
y = -\frac{3}{2}x + 7
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a linear equation?
2. What is the y-intercept of the line \( y = -\frac{3}{2}x + 7 \)?
3. How do you convert an equation from point-slope form to slope-intercept form?
4. How do you find the x-intercept of a linear equation?
5. What is the general form of a linear equation?

**Tip:** When converting between forms of linear equations, always keep track of the slope and intercept values, as they reveal key properties of the line.

Learn how to solve the linear equation y - 1 = -3/2(x - 4) step-by-step. This problem covers the concepts of linear equations and slope-intercept form. Suitable for Grades 7-9.

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