To convert the equation \( y + 3 = -\frac{2}{3}(x - 3) \) into slope-intercept form (which is \( y = mx + b \)), follow these steps:
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Distribute \(-\frac{2}{3}\) on the right side: \[ y + 3 = -\frac{2}{3}x + \frac{2}{3} \cdot 3 \]
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Simplify the right side: \[ \frac{2}{3} \cdot 3 = 2 \] So, the equation becomes: \[ y + 3 = -\frac{2}{3}x + 2 \]
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Now, isolate \(y\) by subtracting 3 from both sides: \[ y = -\frac{2}{3}x + 2 - 3 \]
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Combine the constants: \[ 2 - 3 = -1 \] Therefore: \[ y = -\frac{2}{3}x - 1 \]
The equation in slope-intercept form is: \[ \boxed{y = -\frac{2}{3}x - 1} \]
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