To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) to slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we need to isolate \( y \).
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Start with the original equation: \[ y - 2 = \frac{3}{2}(x + 2) \]
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Distribute \( \frac{3}{2} \) on the right side: \[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \] \[ y - 2 = \frac{3}{2}x + 3 \]
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Now, add 2 to both sides to isolate \( y \): \[ y = \frac{3}{2}x + 3 + 2 \] \[ y = \frac{3}{2}x + 5 \]
Now the equation is in slope-intercept form: \[ y = \frac{3}{2}x + 5 \]
Here, the slope \( m \) is \( \frac{3}{2} \) and the y-intercept \( b \) is \( 5 \).
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