If your partitions are formatted with an
ext filesystem, I'm not very sure that EASEUS Partition Master can handle them.
GParted is another partitioning program you can use, very similar to EASEUS Partition Master.
To resize your
/ and
/home partitions they have to be unmounted. You can't do that while they are in use.
You have to use a LiveCD or USB, boot from it, install GParted from Synaptic and then resize your partitions.
Or you can use the GParted LiveCD
http://gparted.sourceforge.net/livecd.php.