Use I mac 2009 as a monitor

There were at least five 2009 iMac models.

Identify your iMac model - Apple Support

Identify the ports on your Mac - Apple Support

Please read Use your iMac as a display.

That iMac has a Mini DisplayPort and the MacBook Air has Thunderbolt 3 ports.

There are many sources for cables and adapters. Monoprice is one. I am unable to provide a specific recommendation only because I don't happen to have that model iMac (a 20 inch Mid 2009). Start with Monoprice and determine if you can find a recommendation from a reviewer.

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Seems to be a lot of that same question recently. Using iMacs as displays for home schooling I surmise? Anyway check Amazon too, just don't buy one unless you find a reviewer who can confirm it will work with that model iMac. They're inexpensive enough and returnable but you don't want to waste time with one that doesn't work.

One more thing to consider is an external display. Your MBA can support a 5K monitor which is astounding.

Of course that would be orders of magnitude more expensive than a cable, and the iMac's 20" display is much bigger than your MBA's, but it's not that impressive these days.

What the rest of the world calls USB-C Apple calls Thunderbolt 3. It's actually more complicated because Thunderbolt devices require Apple proprietary Thunderbolt hardware.

I suppose Thunderbolt sounds less intimidating, but Apple's efforts to simplify things probably just added to the confusion. But in any event everything we knew as Mini DisplayPort is now Thunderbolt.

HDMI used to be simple too.

Here's the Monoprice page: https://www.monoprice.com/product?p_id=24447

Reviews seem to indicate it'll work.