Abstracting a continuous dynamical system by a hybrid linear automaton allows to use formal verification techniques to check properties of hybrid systems. In order to build the abstract model, the state space is partitioned and the rate of each state variable is approximated. When the system is linear the properties of the continuous system can be used to split the state space in order to get a tighter abstraction with an automaton that remains simple, so that the reachability calculus is more accurate. Moreover the accuracy of the approximation can be used to aid the design of the partition.