Final answer:
The nurse should administer the medication with a syringe next to the tongue for accurate dosage and proper swallowing.
Step-by-step explanation:
The appropriate administration method for the nurse to use when administering a liquid medication orally to a 9-month-old infant is to administer the medication with a syringe next to the tongue. This method allows for precise delivery of the medication and ensures that it is swallowed by the infant.
Other methods such as mixing the medication with the infant's formula in the bottle, allowing the infant to drink from a medicine cup, or administering with a spoon may not provide accurate dosage or ensure that the medication is swallowed properly.
Using a medicine cup is not practical for infants, and administering with a spoon may increase the risk of spillage and inaccurate dosing.