What is the difference in a branch line and a main on a water line?

Perhaps someone closed the water valve or main. It could be a blockage or a pipe collapsed or tree roots clogging it off or corrosion. If it's city supplied water there is a valve out by the curb...

The Minimum is 2 ft. Some places you can put a line in that is only 48 inches under ground. It all depends on what state your in... and the town or city. Up north where it gets cold the put main...

A straight line is the shortest distance between two points, a line is the delineation of a connection between two or more points.

Yes

A line segment has a end point. A ray goes on forever until it hits something, like another ray.