Welcome to the forum.
Turn on your OBJECT SNAP TRACKING and other values as shown in the image of the OSNAP tab of the DRAFTING SETTINGS dialogue box.
After starting your line by selecting the first point, HOVER over the grip which is at the corner of the box.
Do not click on it, and the program will acquire the X value of that point, then move up toward the line you are creating and you will
see a tracking vector generated which will include a snappable point of intersection with your new line.
Turn on your ORTHOGONAL MODE to avoid any issues.
I suppose you could use parametric constraints too, but that is a whole different can of worms
and seems over the top for such a simple case. But you should know that they are available and very good tools.
I have succeeded in making this sound really difficult, which it is not.