You can modify the pivot point of a line, without affecting the slope.

You can edit the pivot point by clicking on the Line while holding the shift key. Grab it and move it.

Screen shot 2011-06-11 at 9.38.35 AM

When you select “Edit Pivot Point”, a guide appears, showing the new position. When you’re satisfied, just click. The line has been moved.

Screen shot 2011-06-11 at 8.43.22 AM

At any time, right-clicking (or Option-click) will cancel the current operation