Final answer:
The term describing false statements that harm someone's reputation is defamation, with spoken falsehoods called slander and written falsehoods called libel.
Step-by-step explanation:
The term for an unjust or untrue statement intended to create a negative impression of someone is defamation. This term encompasses both slander, which refers to false spoken statements, and libel, which refers to false written statements. For a statement to count as defamation, it must be presented as a fact and be capable of damaging someone's reputation or income. In the legal context, those in the media can write negative opinions without falling foul of defamation laws, as long as they do not present these opinions as facts. Legal cases such as New York Times v. Sullivan have established a higher bar for public figures to claim defamation; they must prove that false statements were made with 'actual malice'—knowledge of falsehood or reckless disregard for the truth.