To transform the linear equation \(-2y = 14 - 6x\) into slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), you need to solve for \(y\).
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Start with the original equation: \[ -2y = 14 - 6x \]
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Divide each term by \(-2\) to isolate \(y\): \[ y = \frac{14}{-2} - \frac{6x}{-2} \]
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Simplify the fractions: \[ y = -7 + 3x \]
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Rearranging gives: \[ y = 3x - 7 \]
So, the equation in slope-intercept form is: \[ y = 3x - 7 \]
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