Lets assume that our field $K$ is the Puiseux series. I have been working with tropicalization from the book "Introduction to tropical geometry"
link : https://homepages.warwick.ac.uk/staff/D.Maclagan/papers/TropicalBook20.4.14.pdf
The fundamental theorem of tropical algebraic geometry (page 99) tells us how we tropicalize a variety within an algebraic torus $T^n$. I am interested in the tropicalization of the line $V(ax+by+c)$ where $a,b,c\in K$ within $\mathbb{P}^2$. My problem is I have no idea on how to approach this exercise even thou I know how the set looks. Any help?