To transform the linear equation \(-2y = 14 - 6x\) into slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, follow these steps:
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Start with the original equation: \[ -2y = 14 - 6x \]
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To isolate \(y\), divide each term by \(-2\): \[ y = \frac{14}{-2} + \frac{-6x}{-2} \]
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Simplify the fractions: \[ y = -7 + 3x \]
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Rearrange it for standard slope-intercept form \(y = mx + b\): \[ y = 3x - 7 \]
Thus, the correct slope-intercept form is: \[ \boxed{y = 3x - 7} \]