imac 2007 as dual monitor with mini dvi

Halo all i have an imac2007 with minidvi port and a macbook air with thunderbolt.

If i understand right the old imac works only as output video and not as input video, it is right?

Or can i buy a cable minidvi/thunderbold and use the imac as second monitor?

both hardwares uses yosemithe, it is the sharing screen available via thunderbolt/usb or thunderbolt /ethernet( or minidvi?)

I read about screenrecycle but i prefer to search for another solution.