Is it true that if a particle is moving on a straight line then with negative acceleration the graph of distance vs time will be downwards and with positive acceleration the graph will be upward?

The above statement is true.
Retardation decreases the velocity of an object, and acceleration increases w.r.t. time, so when we draw a graph between distance and time, due to retardation rate of change of distance will decrease so that the graph will be downward, and due to acceleration graph will be upward.