Find the slope of a line perpendicular to the line whose equation is 6x+y=−5. Fully simplify your answer.

Answer 1

To find the slope of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.

First, let's write the equation in slope-intercept form: $y = -6x-5$.

The slope of the given line is $-6$.

So, the slope of a line perpendicular to the given line is the negative reciprocal of $-6$: $\frac{1}{-6} = \boxed{-\frac{1}{6}}$.