Consider a situation in which the observer measuring the linear velocity of a point on equator is standing closer to that point on Earth. According to the observer, the distance between him and the point has not changed over time, therefore there is no relative motion between the two.
Thus, the observer is forced to conclude that the point is stationary, with no linear velocity relative to him.
Now consider that the observer has moved vertically upward through a parachute to a considerable height and the point is still observable from the observer position in space.
The observer will see a significant change in position of the point on the Earth over time because the point drifts from its initial position due to the Earth’s rotation. To the observer, the point now has a linear velocity accounting for his motion relative to observer position in space.
This shows that the linear velocity of a point on Equator is dependent on the position of the observer.