Why doesn't my Mac Book Air have an update for Monterey?
Can I update my MacBook Air to IOS Monterey?
MacBook Air 13″, macOS 10.13
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You can if it is a 2015 or later model.
The model year of a MacBook Air is available at Apple menu > About This Mac.
A late 2010 through mid 2011 MacBook Air can be upgraded to High Sierra 10.13.6 but no later version. See: How to get old versions of macOS - Apple Support
A mid 2012 MacBook Air can be upgraded to Catalina 10.15.7 but no later. See: How to get old versions of macOS - Apple Support
A mid 2013 and early 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to get old versions of macOS - Apple Support
An early 2015 or later can be upgraded to the current version of Monterey macOS 12. See: How to upgrade to macOS Monterey - Apple Support