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We are given the following information about the line:
- The slope \( m = \frac{3}{2} \)
- A point on the line: \( (-4, 6) \)

To find the equation of the line in slope-intercept form \( y = mx + b \), we can use the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
Where:
- \( (x_1, y_1) \) is the given point \( (-4, 6) \)
- \( m = \frac{3}{2} \) is the slope

### Step 1: Plug in the values
\[
y - 6 = \frac{3}{2}(x + 4)
\]

### Step 2: Expand and simplify
Distribute the slope on the right-hand side:
\[
y - 6 = \frac{3}{2}x + \frac{3}{2} \times 4
\]
\[
y - 6 = \frac{3}{2}x + 6
\]

### Step 3: Solve for \( y \)
Add 6 to both sides to isolate \( y \):
\[
y = \frac{3}{2}x + 6 + 6
\]
\[
y = \frac{3}{2}x + 12
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = \frac{3}{2}x + 12
\]

Would you like further details or have any questions?

Here are 5 related questions to extend your understanding:
1. How do you derive the slope-intercept form from a point-slope equation?
2. What is the significance of the y-intercept in the slope-intercept equation?
3. How would the equation change if the slope were negative?
4. How can you graph the equation \( y = \frac{3}{2}x + 12 \)?
5. How can the equation of the line be rewritten in standard form?

**Tip:** When finding the equation of a line, it's useful to always write the equation in point-slope form first, especially when you are given a point and a slope.

A line passes through the point (-4, 6) and has a slope of 3/2. Write an equation in slope-intercept form for this line.

Learn how to find the equation of a line passing through the point (-4, 6) with a slope of 3/2. This solution includes the use of point-slope and slope-intercept forms, suitable for students in Grades 7-9.

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