What do prepositions link words to show?

The correct answer indicates that prepositions link words to show relationships between ideas. Prepositions serve as connectors in a sentence that effectively illustrate how different elements relate to one another within the context of the sentence. For instance, they can clarify how one noun relates to another noun, thus establishing the connection between concepts or actions that are being discussed.

Prepositions often help in establishing the nature of these relationships, such as causation, comparison, or condition. For example, in the phrase "after the meeting," the preposition "after" indicates a temporal relationship between "after" and "the meeting," demonstrating how one idea (the timing) relates to another (the event).

Other options, while somewhat related to prepositions, are narrower aspects of the broader function of prepositions in language. Time relationships and locations indeed can be indicated by prepositions, but they do not encompass the full range of relationships that prepositions express. Emotional states typically rely more on adjectives and do not directly involve prepositions in their function. Thus, the choice highlighting relationships between ideas captures the comprehensive role of prepositions in linking different aspects of language.