  The prototypical examples of tropical compactifications are compactifications
of complements of hyperplane arrangements, which posses a number of remarkable
properties not satisfied by more general tropical compactifications of closed
subvarieties of tori. We introduce a broader class of tropical
compactifications, which we call quasilinear (tropical) compactifications, and
which continue to satisfy the desirable properties of compactifications of
complements of hyperplane arrangements. In particular, we show any quasilinear
compactification is sch\"on, and its intersection theory is described entirely
by the intersection theory of the corresponding tropical fan. As applications,
we prove the quasilinearity of the moduli spaces of 6 lines in $\mathbb{P}^2$
and marked cubic surfaces, obtaining results on the geometry of the stable pair
compactifications of these spaces.
