Your sleep image is typically just a dump of your machine's memory onto the hard drive so that in the event of a power loss you can resume slightly faster than a boot process.  You can safely ignore it.

Typically in my backups the only thing I grab is my Users folder. Occasionally I might be interested in things in /Library/Preferences, but rare is that event. There's nothing outside that system that can't be recovered through other means.  As for applications in /Applications, part of my backup scripts dump an ls of that directory into a file, so I know what I had there in the event of a drive failure, but I don't actively back up what can be reinstalled / redownloaded later.  'Tis a waste of backup space, especially since with new program versions, etc., that data changes quite often anyway.

Can I safely exclude sleepimage from OS X backups
In Back to the Future, Marty goes back to 1955 and devises a plan for his father George McFly to win over Lorraine in order to ensure Marty's survival.

The plan involved Marty pretending to sexually assault Lorraine then George would step in and stop him. Biff meddles with Marty's plan, by kicking Marty out of the car and then he tries to rape Lorraine. George expecting to find Marty in the car, instead finds Biff and musters the courage to stop Biff and protect Lorraine.

Near the end of the movie when Marty travels back to 1985 we see that Biff is outside of Marty's house waxing George's car. Why would George employ Biff to do this job? I can't imagine Lorraine would be too happy with the idea.
