How do you stream IMac 2007 to AppleTV?

from Apple docs:

Requirements for AirPlay in OS X

An Apple TV;

• Apple TV (2nd or 3rd generation) with software update v5.0 or later. See How to update Apple TV software.
• Airplay turned on in the Settings menu of the Apple TV.

A supported MacAirPlay Mirroring in OS X takes advantage of the hardware capabilities of recent Macs to deliver high frame rates while maintaining optimal system performance. The following Mac models support AirPlay Mirroring::

• iMac (Mid 2011 or newer)
• Mac mini (Mid 2011 or newer)
• MacBook Air (Mid 2011 or newer)
• MacBook Pro (Early 2011 or newer)
• Mac Pro (Late 2013)

For a long time, my dad's iMac 2007 (running under some old intermediate Mac OS X) was successfully AirPlaying to an AppleTV. It was actually running smoothly, and we could see videos on webpages.

But when I upgraded it to Mavericks, the AirPlay feature disappeared.

(iMac mid-2007 happens to be the oldest Mac that still suppots Mavericks/Yosemite). I guess Apple started enforcing the minimum system requirements, even though the 2007 iMac certainly definitely had the graphical horsepower to successfully AirPlay to the AppleTV. Maybe because the older laptops didn't have the graphical horsepower, but the desktop does. Yes, it was a 2007 iMac, and yes, it was Apple's AirPlay rather than AirParrot or other third party app.

The requirement was always in place, the mirroring feature relies on a feature only available in the newer processor in order to do real time video encoding.