Afootball is thrown at an angle of 30.° above the horizontal. the magnitude of the horizontal
component of the ball’s initial velocity is 13.0 meters per second. the magnitude of the vertical
component of the ball’s initial velocity is 7.5 meters per second. [neglect friction.]
draw a graph representing the relationship between the horizontal
displacement of the football and the time the football is in the air.

If we ignore air resistance (which we always do), then the
vertical component has no effect on the horizontal component. 
What we have is just a football that's moving horizontally at
13 meters per second, and we don't care what it's doing vertically.

The graph of the football's horizontal position vs time, for as long
as it remains in the air until the ground comes up and grabs it is:

-- a straight line

-- the slope of the line is 13 m/s .
 
-- If we start the clock at the instant the ball is tossed and
    call that time=0, then the line passes through the origin.
   (We probably don't care where the ball is before it's tossed,
     so we can just as well begin the line at the origin.)

The particles of the gas inside the ball heats up, bouncing off each other and spreading farther apart.hope my answer has you : )

'b ' is the correct conclusion.