To transform the equation \( y - 6 = 2(3x + 8) \) into slope-intercept form (\( y = mx + b \)), follow these steps:
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Distribute the \( 2 \) on the right side: \[ y - 6 = 2 \cdot 3x + 2 \cdot 8 \] \[ y - 6 = 6x + 16 \]
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Add \( 6 \) to both sides to isolate \( y \): \[ y = 6x + 16 + 6 \] \[ y = 6x + 22 \]
Thus, the equation in slope-intercept form is: \[ y = 6x + 22 \]
In summary, \( m = 6 \) and \( b = 22 \): \[ y = 6x + 22 \]