The equation of the line is $3x - 3\sqrt{2}y - 7 = 0$. We can rewrite this in the form $y = mx + c$ to find the slope $m$.
\[
y = \frac{3x + 7}{3\sqrt{2}} = \frac{\sqrt{2}}{2}x + \frac{7}{3\sqrt{2}}
\]
So, the slope of the line is $m = \frac{\sqrt{2}}{2}$.
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