To convert the equation \(2y = 6x + 2\) into the slope-intercept form \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept, you can follow these steps:
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Start with the original equation: \[ 2y = 6x + 2 \]
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Divide every term by 2 to solve for \(y\): \[ y = \frac{6x}{2} + \frac{2}{2} \]
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Simplify the equation: \[ y = 3x + 1 \]
Now, the equation is in the form \(y = mx + b\), where \(m = 3\) and \(b = 1\). Thus, the slope is 3 and the y-intercept is 1.