Each point has a numerical attribute that I would like to transfer to the line (The lines represent directional data). I broke already the line at each point, but I don't know how to transfer the attribute from each point to the line. Does anyone know how to do it?
Spatial Join could work for this. HERE is the documentation.
However seeing how one point touches two line segments how are you deciding which point attributes will be joined? (two points will be touching the same line segments...)