Hello, first post and I wanted to make a similar thread but I might as well post here.
It's definetly not normal because I have the same issue but just now (temporary I think) fixed it.
First I fixed it by disabling AMD Overdrive but somehow that fix did not stick. (This seems to be the most common solution found on the net)
And right now I used the Windows 7 settings to duplicate the screen and the tearing line is gone. I do not mean the Windowskey+p shortcut but going into the control panel to display options and duplicate the screen from there.
What worries me is this solution might be temporary just like the first time I fixed it. Another thing which worries me is I've been using google and seeing threads about the same issue dating back to 2010!
There is definetly a bug in the driver.
When the tear line was there I could make it switch screens.
The screen which I made preferred would not have the line.