Q: Using airplay prism 10 mb

Not entirely sure what you mean.

Could you perhaps explain what is going on?  What do you mean by "prism"

What are you AirPlaying?

AirPlay will not vary due to the ISP speed.  ISP is used when sending data away from your network or downloading data to your network I.e. Sending email or streaming Netflix. AirPlay uses the local network to stream content locally.  As Prism is an Internet provider that shouldn't matter. What will matter would be the router that the ATV and the AirPlay device are connected to and the services running locally like multiple users, or multiple devices.  Also look at background processes like firewall, spam etc.  lastlty there can always be local interference issues for example, the forest department installed a pump near my property and my wifi was impacted every hour for about 5-10minutes Intervals...

Which ATV do you have?  What device are you attempting to AirPlay from?  Not all devices support AirPlay video...

That being said, with a 10mb connection to ISP you may encounter issues with streaming and/or slow download.  it may work depending on how stable that speed remains.  Though streaming providers like Netflix, Hulu etc will require a lesser speed due to the variable compression they employ....

Get help playing or streaming content on your Apple TV - Apple Support

To stream content, we recommend a broadband Internet connection and these connection speeds:

• 8 Mbit/s or faster for 1080p high-definition content
• 6 Mbit/s or faster for 720p content
• 2.5 Mbit/s or faster for standard-definition content

You should check the ports TCP and UDP ports used by Apple software products - Apple Support

i also found this older post that may be helpful - AirPlay Actiontec CenturyLink

also, make sure the software is up to date with all devices (router, iphone, iPad, ATV). Disable IPv6 on the router if applicable...