I will present part of the results in the paper “Using separation algorithms to generate mixed integer model reformulations” by R. Kipp Martin (1991). We will see a general technique for obtaining extended formulations for problems whose separation problem can be formulated as a linear program. Throughout the whole discussion we will keep revisiting the Minimum Spanning Tree (MST) case. In the end, we will also see a connection between the obtained extended formulation for MSTs and slack matrices. This last part is based on the classical paper of Yannakakis “Expressing Combinatorial Optimization Problems by Linear Programs”.