To convert the equation \(6x - 3y = 15\) 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: \[ 6x - 3y = 15 \]
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Isolate the term involving \(y\) by moving \(6x\) to the right side: \[ -3y = -6x + 15 \]
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Now, divide every term by \(-3\) to solve for \(y\): \[ y = \frac{-6x}{-3} + \frac{15}{-3} \]
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Simplify the fractions: \[ y = 2x - 5 \]
So, the equation in slope-intercept form is: \[ \boxed{y = 2x - 5} \]