What monitor can be used with a Mac laptop?

Depending on the vintage of your Mac and the ports built into it..

Some may require newer Adapters; others may need PD or 'power

through' to run products; which may require both power and data.

See • About the video ports on Mac - Apple Support

https://support.apple.com/guide/mac-help/about-video-ports-cpmh0014/10.14/mac/10.14

[Varies & depends on build year Mac, and its ports.]

There are several Support articles to help use and troubleshoot

issues that some users found with external displays. These vary

depending on the port types, on each end. With Mac 'in charge.'

• Use multiple displays with your Mac - Apple Support (varies shows many macOS)

https://support.apple.com/guide/mac-help/use-multiple-displays-mchl7c7ebe08/10.14/mac/10.14

• Adapters for the Thunderbolt 4, Thunderbolt 3, or USB-C port on your Mac - Apple Support

https://support.apple.com/en-us/HT207443

• Connect a display to your Mac - Apple Support

https://support.apple.com/en-us/HT202351

• If your external display isn't detected or appears blurry on your Mac - Apple Support

https://support.apple.com/en-us/HT201177

• Connect a display, TV, or projector to Mac - Apple Support

https://support.apple.com/guide/mac-help/connect-a-display-tv-or-projector-mchl5fdd37ce/10.14/mac/10.14

• Identify the ports on your Mac - Apple Support

https://support.apple.com/en-us/HT201736

Some televisions use way different connectors; their adapters may be simple or complex.

Given to me, includes a cable. Never been attached to my Mac. No room for larger display.

(And TV is new/old stock still in the box.)

Good luck & happy trails! ☺︎

PS: Because you've not identified which one of dozens MacBook Air 13-in build year models

this would help discover which one you have; to match display port output to certain third

party external displays; the task is gigantic. ~ Most displays require the correct adapter.

You have 'identifiers' built into the device; all Macs do.

[We do not need nor want any serial numbers.]

• Lookup Mac Specs by the Numbers | everymac

https://everymac.com/ultimate-mac-lookup/

This works well help many details about Macs.

Don't post any serial numbers they'll be removed.

By year everymac.com has most every build model Macintosh from the beginning.

https://everymac.com/systems/apple/macbook-air/index-macbook-air.html

Also this article from Apple Support has some details that could help. [I've to figure

your Mac is a MacBook Air. Only due to your post's signature line ~ shows one there.]

• Identify your MacBook Air model - Apple Support

https://support.apple.com/en-us/HT201862

The models in article by year -- run from 2009 -- to those in production this year.

(Everymac covers details; except for rarer custom build variants within model yrs.)