Macbook Air not detecting LG ultra wide monitor resolution

I have an LG ultra wide monitor (29WK50S) and my Mac will only run at 1920x1080 on the monitor even though the native resolution of the monitor is 2560 by 1080. This results in a stretched out image. When I go to display settings, there is not an option to choose 2560x1080 for the monitor, even when I hold the option key to view more resolutions. I have a mid 2013 MacBook Air and I am using a Belkin mini-display port to HDMI adapter. What is the problem?