1) using no shift.
Click line tool in drawing tools, cursor turns into "+" (without quotes)
Left click on body page, no handle appears, but as one moves some distance away, scraggled line appears from first click. Second click and line appears with black handles.
3) Using shift after start
Click line tool in drawing tools, cursor turns into "+" (without quotes)
Left click on body page, holding down clicker, then hold down shift, line completely disappears.
2) Using shift before start. Works perfectly!
Thanks 
We seem to be talking about different things. I thought you were concerened about editing the line after it was drawn.
For creating a new vertical/horizontal line, select the line tool (cursor becomes +), and then hold down the shift key. Now click where you want to start (while still holding the shift key) and then drag the line to where you want it to end (i.e. your last approach). At this point it will still be the selection and show the handles at both ends.
For editing and existing line, ctrl+click on the line. The handles will appear. Hold down the shift key and then click on th handle that you want to edit. You can drag it either horizontally or vertically along the imaginary axis going through the selected end-point while using the shift-key modifier.