The observation of the electroweak production of single-top-quarks is made using 255 pb-1 of proton-proton collision data recorded at √s=5.02 TeV with the ATLAS detector at the Large Hadron Collider. An event selection is used to identify single-top-quark candidates arising from t-channel production with the top quark decaying semi-leptonically. Events passing the selection are then used to measure the inclusive cross-section for the combined production of single-top-quarks and antiquarks and the ratio between these two. All measurements are in good agreement with the Standard Model predictions.