To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:
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Distribute \(\frac{3}{2}\) on the right side:
\[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \]
This simplifies to:
\[ y - 2 = \frac{3}{2}x + 3 \]
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Now, add 2 to both sides to isolate \( y \):
\[ y = \frac{3}{2}x + 3 + 2 \]
Simplifying further gives:
\[ y = \frac{3}{2}x + 5 \]
So, the equation in slope-intercept form is:
\[ y = \frac{3}{2}x + 5 \]
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