Unigrass 6600 drawer slides with t-rivet

A home owner from Phoenix says:
Hi!
We are looking for drawer slides that have a t-rivet on both ends that fit into a slotted rail (I don't know what this system is called). This is for slide-out shelves inside cabinets. This system makes it easy to adjust the shelves up or down. The sliders are 22 in. in length and we need at least 4 sets of them. These slider have "Unigrass 6600" printed on them, but the ones I find online are missing the rivet to fit in the slots. If you know what this system is called, please let me know. Any help is greatly appreciated!
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Emily from SWISCO responded:

Hello!

We don't carry your exact drawer slides but take a look at our 32-061 or 32-062. Just note, our slides are designed to screw in and they won't be able to clip into the fitting rail you have now. Look this over and see what you think. 

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