Another approach uses rasterize method from Processing Tool Box and Raster Calculator. In my example, I used line vector layer and slope raster of next image:
For rasterizing, you first need these raster parameters (see in Metadata Properties) from original raster:
Layer Extent (layer original source projection)
However, 'Layer Extent' is not in order required for rasterize tool. Must be ordered as: xmin, ymin, xmax, ymax.
In my case, these parameters were:
354971.3488602247089148, 479272.4038835020037368, 4414903.3223166307434440, 4473428.4023900907486677
and they were copy/paste at rasterized tool as in next image (id in line vector layer must be 1):
After run, I got this rasterized line (pseudocolor with 2 classes and transparency for 0 values). This one is perfected aligned with original raster.
Finally, I used next formula in 'Raster calculator expression':
( "Rasterized@1" ) * "utah_demUTM2_slope@1"
to get a new rasterized line; but with slope values instead. Red rectangle at next image point out your required statistic parameters, average and maximum slope, for this vector line.