Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 6, y, equals, minus, 723x−6y=−72.
To find the slope of a line perpendicular to another line, we take the negative reciprocal of the slope of the given line.
The given line has the equation $-723x-6y=-72.$ We can rewrite this equation in slope-intercept form: \begin{align*}
-6y&=723x-72\\
y&=-\frac{723}{6}x+12\\
y&=-\frac{241}{2}x+12.
\end{align*} The slope of this line is $-\frac{241}{2},$ so the slope of a line perpendicular to this line is $\boxed{\frac{2}{241}}.$