Find the slope of a line perpendicular to the line whose equation is 3, x, plus, y, equals, minus, 93x+y=−9. Fully simplify your answer.
To find the slope of the line, we need to rewrite the equation in slope-intercept form: $y = mx+b$, where $m$ is the slope. We have the equation $-93x + y = -9$. We can rewrite this equation as $y = 93x - 9$. Comparing this with $y = mx+b$, we see that $m=93$ is the slope of the line.
A line perpendicular to this line will have a slope that is the negative reciprocal of $m$. The negative reciprocal of $93$ is $\boxed{-\frac{1}{93}}$.