  Using elementary ideas from Tropical Geometry, we assign a a tropical curve
to every $q$-holonomic sequence of rational functions. In particular, we assign
a tropical curve to every knot which is determined by the Jones polynomial of
the knot and its parallels. The topical curve explains the relation between the
AJ Conjecture and the Slope Conjecture (which relate the Jones polynomial of a
knot and its parallels to the $\SL(2,\BC)$ character variety and to slopes of
incompressible surfaces). Our discussion predicts that the tropical curve is
dual to a Newton subdivision of the $A$-polynomial of the knot. We compute
explicitly the tropical curve for the $4_1$, $5_2$ and $6_1$ knots and verify
the above prediction.
