First of all, I have a Line 6 Spider III 15 watt. I noticed it had a recording/line out jack on the right side of the amp so I figured I'd hook it up to my laptop and see if I could record some stuff.

The way I ASSUMED I could do this is by plugging a 1/4'' - 3.5mm male-female adapter straight into the amp, then running a 3.5mm-3.5mm male-male cord from the adapter straight to the microphone jack on my computer.

Is this even possible? I haven't tried it yet because I don't have the right cord, and I don't want to spend any money if I don't need to.

If this is possible, how? Thanks for any help.
Yeah, that's how I record with my POD, only minus the adaptor. My brother records with his Cube like that.
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Thats exactly how i record. I run an RCA cable (red and white cable) with a 1/4" jack going to the amp and a 1/8" jack going to my laptop. Its 3 pieces you need to buy and you can pick it all up at radio shack for like $25