Agraph shows distance on the vertical axis and time on the horizontal axis. if the speed is steadily increasing, what will the line representing speed look like on the graph?

Wait just a minute.  You said it's a distance/time graph, so there's no line on it
that represents speed.  The line represents distance.

If the speed is steadily increasing, then as time goes on, more and more distance
will be covered during each unit of time.  The distance line on the graph will
curve upward, more and more steeply as time goes on.  If you put a ruler against
the curve, then as time goes on, the slope of the ruler gets bigger and bigger,
because the slope at any point on a distance/time graph is the speed at that time. 

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.