To rewrite the given equation \( y + 10 = \frac{3}{2}(x + 4) \) in slope-intercept form (which is \( y = mx + b \)), we need to isolate \( y \).
First, distribute \(\frac{3}{2}\) on the right side:
\[ y + 10 = \frac{3}{2}x + \frac{3}{2} \cdot 4 \]
Calculating \(\frac{3}{2} \cdot 4\):
\[ \frac{3}{2} \cdot 4 = 6 \]
Now, substitute this back into the equation:
\[ y + 10 = \frac{3}{2}x + 6 \]
Next, subtract 10 from both sides to solve for \(y\):
\[ y = \frac{3}{2}x + 6 - 10 \]
This simplifies to:
\[ y = \frac{3}{2}x - 4 \]
Now we have the equation in slope-intercept form:
\[ \boxed{y = \frac{3}{2}x - 4} \]