can i back up my macbook to my imac's hard drive?

That would be an absolutely terrible idea! If you have a problem with your iMac you may likely lose the files and, unless you actually managed to partition that drive for the backup, it is still a very bad idea. Besides, if you intend to use time machine, you need to have enough empty room 2 - 3 times the size of the macbook drive.

So, buy an external hard drive for your backups.