I have two 'base' line features that are somewhat parallel to each other, which are connected by vectors (also line features) [Check attached photo - underlying raster layer is not the DEM].

I want to use the vectors connecting the two 'base' lines to extract slope values calculated from a DEM. In other words, the vectors connecting the two 'base' lines are spatial sampling units, which will be used to extract topographic information to describe the movement from one base line to the next. This is obviously problematic, since ArcGIS's slope tool only calculates slope directionality in terms of a convolution 3x3 kernel, which in turn, gives an output in degrees or percent rise....So. When I use the vectors to extract the slope values along each one (individual vectors), there are obviously no negative values, when in reality, these vectors all have some sort of mixture of negative and positive slopes ( because many of the vectors from base line 1 to base line 2, go up and then down slope, or vice-versa).

My question - What algorithms can I use to transform the slope values based on some relative starting point of each vector, so that once I extract the slope values from each vector line - it will illustrate whether that vector was going predominantly downhill (negative slope) or uphill ( positive slope)?

Thank you for your time. Any thoughts, comments, or recommendations are greatly appreciated.

You say you don't have the DEM? Can you not get the one used to produce the slope raster? or a surrogate for the area? The solution would be to find that data to extract the elevation values.

Do you have a curvature raster? Curvature—Help | ArcGIS Desktop which would at least provide some information on slope directionality