Normal line: $-5$ or $\frac{1}{5}$?

Question

Find the equation of the normal line to the graph of $f$, $f(x) = \ln(x + 1)$, so that the normal line is parallel to the line $y = −5x + 101$.

Here's the formula for finding normal line: $y - y_{0} = \frac{-1}{f'(x_{0})}(x-x_{0})$

I am simply wondering: when considering the coefficient $\frac{-1}{f'(x_{0})}$, should I treat it as $-5$ or $\frac{1}{5}$? $-5$ seemed obvious to me, because it's parallel to $y=-5x+101$, but I'm not sure if I'm right.

Thanks!

Answer 1

Yes, $-5$ is correct - parallel lines do not intersect, and this can only happen if they have the same slope / gradient. It would be $\frac15$ if you were asked to find a line that is perpendicular to the line with slope $-5$.