you can store the image of the picturebox before you draw the verticle line, and then just reset it when you want.

Code:
'Put code here to draw the curve in the picturebox


'This stores the image in the picturebox's memory
Set Picture1.Picture = Picture1.Image



'now draw the vertical line here


'When you want to get rid of the verticle line just use
Picture1.Cls

and your curve will still be there because the picturebox has remembered it

obviously you don't have to do this all in one subroutine, you can do the parts whenever you like, when you Set Picture1.Picture = Picture1.Image it stores the image, when you .Cls it restores whatever is stored


to get rid of the curve from the picturebox's memory use

Code:
Set Picture1.Picture = Nothing
Oh, make sure the picturebox's AutoRedraw is set to true, otherwise it won't work