Here's why:

* Electronegativity: Fluorine is much more electronegative than bromine. This means that the bonding electrons are pulled more strongly towards the fluorine atom.

* Lone Pairs: Bromine has 7 valence electrons, and it forms a single bond with fluorine. This leaves 3 lone pairs on the bromine atom. These lone pairs are located in the same plane as the Br-F bond, which is a common arrangement for halogens.

* VSEPR Theory: According to VSEPR theory, the electron pairs (bonding and non-bonding) arrange themselves to minimize repulsion. In the case of BrF, the most stable arrangement is linear, where the lone pairs are as far apart as possible from each other and the Br-F bond.

Therefore, the shape of bromine monofluoride is linear.