I think the backslash is a notational shorthand for writing either:
The decision affects people at large and the people in general
It's somewhat imprecise because it implies that the two "peoples", people at large and people in general, are exchangeable terms, which makes the sentence redundant. Stylistically, I would encourage something more specific. For instance,
Prohibition affected livelihoods of all American people.
"at large" and "in general" are prepositional phrases, and they modify the people because
- they are placed at the end of the sentence
- the "people" is a subjective noun, and "affects" is used as a transitive verb
- It doesn't make sense to "affect at large" as a verb or for a "decision at large" to be a noun
- practically, the sentence is trying to emphasize that the implications of a certain policy or action will perhaps have more wide ranging implications that initially assumed.