Just start an edit session in ArcMap on the layer that the line is going into. Select the line feature. Right click and copy and then right click and paste. A dialogue should open up and prompt you to choose the layer you want to paste it to. I believe you should be in 'data view' to do this, not 'layout view'
Alternative way is in your data table add a field such as "Edited" when you do your edit enter a X in the field. set you symbology to change the color of Edited = X to a different color than the unedited objects. At the end of a editing session you could query all edited or not edited and save the result to a new file which will carry all the data along. I'm using Map3D2014 & ArcMap10.2.