Final answer:
The nurse should stress the importance of always carrying sublingual nitroglycerine with them, as it's essential for the immediate treatment of chest pain by vasodilation of coronary vessels.
Step-by-step explanation:
When teaching a client with a new prescription for sublingual nitroglycerin, the nurse should emphasize the importance of carrying the nitroglycerine with them at all times. This medication is used for the immediate treatment of angina pectoris (chest pain) by facilitating its absorption under the tongue. Nitroglycerin acts as a vasodilator, releasing nitric oxide and endothelium-derived relaxing factor, which helps to relax the smooth muscles in the coronary vessels and improve blood flow to the heart muscle.