Question

What does the slope of the line on this velocity versus time graph represent?

Answer 1

What do you mean when you say "this" graph ?  I don't see any graph.

First of all, I'm sure you don't have a "velocity versus time" graph.
You may have a "speed versus time" graph, that doesn't show any
information about the direction of the motion.

As you look at your graph ... a feat that's impossible for me ... 

-- If the line is horizontal, then speed is not changing.  If the direction
of motion is also not changing, then there is zero acceleration.  Sadly,
the graph most likely doesn't carry any information about the direction. 
It's possible that the speed is constant but the direction is changing.
Then acceleration isn't zero, but you can't tell that from the graph.

-- If the line is proceeding upward from left to right, whether it's straight
or curving, then there is positive acceleration.

-- If the line is proceeding downward from left to right, whether it's straight
or curving, then there is negative acceleration, or what some people might
call "positive deceleration".