What would the instantaneous velocity be on this graph at
t = 4.5s and t = 7.5 s

This graph represents the position x as function of time t. The instantaneous velocity is given by the derivative dx/dt, which corresponds to the tangent direction in the graph.

From the graph you have a flat line between t=4s and t=5s, thus at t=4.5s the instantaneous velocity is 0. For t=7.5s I will assume that at t=7s you have x=-5m, while at t=8s you have x=0. From t=7s to t=8s you have a straight segment. Thus the instantaneous at t=7.5s is 5m/s.

[QUOTE=Aurora2000;3008427] The instantaneous velocity is given by the derivative dx/dt, which corresponds to the tangent direction in the graph.[QUOTE]

A simpler explanation, as a would guess that the OP hasn't studied derivatives yet: velocity is the change in position per unit time, which means it's equal to the slope of the position-versus-time graph.