To change which image shows up on Facebook, you must add the correct meta attributes. Steps to correctly configure the meta data can be found on Facebook's tutorials here:
https://developers.facebook.com/docs/web/tutorials/scrumptious/open-graph-object/

For non-site specific document on meta data for social networking:
http://ogp.me/

To verify how your site will show up on Facebook, go to https://developers.facebook.com/tools/debug and input your url.