In this work, we propose a novel data-driven representation for general linear time-invariant (LTI) systems based on behavioral system theory. This representation relies solely on input-output data, eliminating the need for exact knowledge of the system structure. We also develop stabilizing controllers and finite/infinite horizon optimal linear quadratic (LQ) controllers using this data-driven representation. In the presence of noise-corrupted data, we present a certainty-equivalence LQ controller and demonstrate its effectiveness through performance analysis and a numerical example.