Yes. Once you let go, the eraser falls straight down along a vertical line until it hits the floor. Its path is a straight line, so this is linear motion.
When an object moves along a straight line,
its motion is called linear motion.
What to observe carefully: hold the eraser still, then simply open your fingers — do not throw it sideways. Watch the path from the side. It goes straight down, and it lands directly below the point from which it was released.
Why it falls straight: the Earth pulls every object straight down towards its centre. If nothing pushes the eraser sideways, there is no reason for it to drift left or right, so the path stays a straight vertical line. (Notice that the speed increases as it falls — but the type of motion is decided by the shape of the path, not by the speed.)
Try This: Drop the eraser and, at the same instant, throw a second eraser sideways from the same height. The dropped one moves in a straight line; the thrown one follows a curved path. Only the first is linear motion.