Four. (25 points)
As shown in Figure 4, in the Cartesian coordinate system, points $A$ and $B$ are two points on the graph of a certain linear function, satisfying $\angle A O B=90^{\circ}$, and $A O=B O=2$. If the angle between $A O$ and the $y$-axis is $60^{\circ}$, find this linear function.