Is it possible for a distance-versus-time graph to be a vertical line

Yes it is possible only if the x axis is distance and the y axis is time, providing the object being monitored or graphed never moves and you are utilizing a line graph for the assignment. time will increase (traveling vertically on the y axis or up/down on the graph) and distance will stay at a constant 0 (not traveling horizontally the x axis or left/right on the graph)

Not the way we generally draw graphs ... with time on the x-axis
and distance on the y-axis.

A vertical line would mean ...

-- The object is a every different distance all at the same time.

-- The object moves from one distance to another in zero time.
   That's the same thing as saying its speed is infinite.

Both of these are definite no-no's.  So you will never see the position
(distance) of a real moving object graphed as a vertical line.

Because the dept in the ocean

Amethod of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.