Drawing a line feature at a constant slope using elevation data?

[Hemlock_Grove]

I build trails that need to meet certain accessibility requirements. One of the requirements is having a certain running grade (slope). 

I have used 2ft. contours and some basic math in the past to get a rough idea of how conducive a terrain is to meeting said requirements, but I am wondering if there is a more precise and/or automated way to draw a line that crosses contours (or uses a DEM layer?) at a constant steady slope.

For example, if I wanted to draw a trail that traverses a hillside at exactly 10% grade, could I utilize elevation data to construct this?

I'm a somewhat novice Arc user, so highly advanced/custom methods are probably out for me. Thank you!

[Hemlock_Grove]

Let me ask this question a little differently, hopefully with it leading to a more straight forward answer:

Is it possible to calculate/determine the slope of line feature, even if the line feature is just arbitrarily drawn? And by line I suppose I really mean a straight line (slope between two points). I know it's possible to draw a slope/aspect model with DEM, but the lines I would be drawing traverse these slopes.