The student plotted distance v. s time graph in which the line sloped downward. is the graph correct?

It could be, depending on WHAT distance was graphed,
and how the student labeled the graph's axes.

Most likely, however, she probably drew the graph ...

-- with time on the x-axis increasing to the right,

-- with distance on the y-axis increasing upward,

-- to show the distance FROM the starting point
   NOT the distance remaining to the destination. 

If that's how she set it up, or if any two of these items are
the other way around, then the line could not slope downward. 
THAT would say that the distance from the starting point is
decreasing as time goes on, or the distance remaining to the
destination is increasing as time goes on.  That would be silly.