If the line on a distance versus time graph and the line on a speed versus time graph are both straight line going through the origin, can the two graphs be displaying the motion of the same object?

No they cannot

Explanation:

A straight line going through the orign in a distance versus time graph would show that the object is going at a constant speed, meaning that the speed is not changing.

A straight line going through the origin in a speed versus time graph would show that the object is accelerating at a constant rate, or that it's speeding up/slowing down at a constant rate

I think the answer is number a burning natural gas release