If the sun were the only object besides Earth, then Earth would move in a straight line, tanget to its position in its orbit when the Sun disappeared.
But Earth is not the only object in the Universe besides the Sun. The moon, for example, would continue to be controlled by the Earth's gravity, and the gravity of the moon would cause Earth to wobble back and forth as the two traveled away from the sun. That track, then, would be a "wiggly" straight line.
The average track of the Moon and Earth would not be a straight line, either. The other planets would tug at us and cause other curvatures in our path. Moreover, we would continue to move in a more-or-less circular path around the center of the Milky Way galaxy which is itself moving through space.
I would bet that none of the above are meant to be considered as a part of your answer, but if it's an essay question you might wish to mention all the other factors besides the Sun that would then modify what would otherwise be a tangential path, as I explained in the first paragraph.
