The nanoscale size and controllable memristance of Memristor (MR) have shown evident superiorities for structuring new integrated circuits with different functions. With regards to the reported MR based filters, their cut-off frequencies could be hardly hot-line controlled on purposes. In this paper, by using the boundary values of memristance, a method for hot-line adjusting cut-off frequencies is newly proposed by inputting a preset DC voltage together with the to-be-filtered signal, without the requirement of extra memristance write circuits, which is hence beneficial for integrated implementation. The floating MR emulator is firstly presented and the saturation operation of its memristance is interpreted. A family of MR based low-pass filters with controllable cut-off frequency are proposed by combining the connection nodes of a memristive circuit network Z with the op amp. Two circuits of the low-pass filter family are chosen for demonstration, and the cut-off frequency and passband gain are calculated. Square and sinusoidal voltage signals are used to test the performance of the proposed low-pass filter family. Both the simulation and experimental results show that the proposed filters can achieve cut-off frequency adjustment with good filtering performance.