I'll have to make the assumption that all of the line on one side of the plate IS visible, and all of the other side is NOT visible (so assuming the line doesn't 're-appear' from behind the plate).
Then, figure out which end of the line segment is on the other side of the plate to you. It should be the one which is furthest from you, and also further from you than the plate-line intersection point is.
Now, the length of line which is hidden by the plate will be the length of the line segment between the HIDDEN end of the segment and the plate-line intersection. Divide this length by the TOTAL length of the line segment, from end to end, and you should get some number between 0 and 1 (well, it WILL be between 0 and 1, otherwise something's broken). If this number is, say 0.56, then 56% of the line segment is hidden.
But just be aware of that assumption I made at the start.
BTW not entirely sure if this is calculus, someone might want to check.