To find the slope of a line parallel to the line given by the equation \(3x - y = 1\), we first need to rewrite the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) represents the slope.
Starting with the equation:
\[ 3x - y = 1 \]
We rearrange it to solve for \(y\):
\[ -y = -3x + 1 \]
Multiplying through by -1 gives:
\[ y = 3x - 1 \]
From this equation, we can see that the slope (\(m\)) of the line is \(3\).
Since parallel lines have the same slope, the slope of any line parallel to this one is also \(3\).
Thus, the slope of a line parallel to \(3x - y = 1\) is:
\[ \boxed{3} \]
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