QGIS - Join polygon layer attributes to line segments

Question

I've got a hexagon layer with data that I want to have joined to the available road network for the area so that the road segments have the attributes from the hexagon layer.
Each segment of the road layer is comprised by the intersection of two roads, there are a total of 304 features. The features that go through multiple polygons should account for the average value of these polygons. Say that H_1 = 0.4 and H_4 = 0.2 (whereas H -> hex polygon bin) thus, (H_1+H_4)/n (where n the number of polygons that intersect the line layer).
How can I do that?

perrier · Answer

SOLUTION:
Intersection with the road layer in regards to the hexagon layer served the purpose well without complicating things too much.
Conversion of comparison of the two layers was conducted as follows (added for replicability purposes):
Vector -> Geoprocessing Tools -> Intersection 
Input layer: road layer 
Overlay: Hexagon bins
Input fields: ID 
Overlay fields to keep: variable (I wanted to assess per road network just
a single variable)

QGIS - Join polygon layer attributes to line segments

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