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), follow these steps:
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Start with the original equation: \[ -2y = 14 - 6x \]
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Divide every term by \(-2\) to solve for \(y\): \[ y = \frac{14}{-2} - \frac{6x}{-2} \]
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Simplify the fractions: \[ y = -7 + 3x \]
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Rearrange the equation to put it in the slope-intercept form: \[ y = 3x - 7 \]
Now, the equation \(y = 3x - 7\) is in slope-intercept form, where the slope \(m\) is \(3\) and the y-intercept \(b\) is \(-7\).