In the provided image, the line is close to, but not truly perpendicular to the edge. Makes me think the line is the edge of the film canister, which would then make me think of some type of light fogging/light leak? Not anything I would automatically think of as a light leak, but it's the only thing I could come up with.
As pointed out above, it can't be a shutter issue. And as also stated, a developing issue would result in all images being affected.
So I'll say some type of light leak. And the longer a frame sits waiting for it's turn at the exposure, the more pronounced it will be. The less time between frames, you may not even see it.
Was the example shot the first of x after a re-posing, a break, or maybe it was the first frame?