To find the slope of a line parallel to the equation \(3x - y = 1\), we first need to express the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) represents the slope.
Starting with the equation:
\[ 3x - y = 1 \]
We can solve for \(y\):
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Subtract \(3x\) from both sides: \[-y = -3x + 1\]
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Multiply everything by \(-1\) to solve for \(y\): \[y = 3x - 1\]
From the slope-intercept form, we can see that the slope \(m\) of this line is \(3\).
Since parallel lines have the same slope, the slope of a line parallel to \(3x - y = 1\) is also:
\[\boxed{3}\]