‘Would rather’ suggests what the speaker prefers. ‘Would rather’ is somewhat similar to ‘Would prefer’.  After ‘Would rather’ we use headless infinitive (i.e bare root verb without’to’.  But after ‘Would prefer’ the root verb is preceded by ‘to’.  To explain further ( would rather do something than do something else)

EXAMPLES

• A:  What would you rather have , tea or coffee?
• B:  I would rather have coffee.
• A:  What would you suggest we should do, go for the film or see the football match.
• B:  We would rather go for the film.
• I would rather sit on the mat.  I don’t want that chair.
• I would rather have two half-boiled eggs and a cup of milk for breakfast.
• I would rather go swimming in the evening.
• What would rather do in your leisure time? Swimming or fishing?
• I would rather go fishing in my leisure time.

Would rather = would prefer (COMPARED)

• I would rather go to the office than sit idle at home. (would rather GO)
• I would prefer to go to the office rather than sit idle at home.(would prefer TO GO).
• I would rather go by train.( simply Go)
• I would prefer to go by train.( To Go).
• He would rather have the small toy than the big one.

Note:- The negative is ‘Would rather not’ do something.

• A: Would you come with us for a movie?
• B: Thank you, but I would rather not.
• It’s raining outside.  I would rather not go out.

*