This is eMachines Support, and the specifications page for the eMachines C6535 desktop computer,http://www.emachines.com/support/product_support.html?cat=Desktops&subcat=C%20Series&model=C6535
Scroll down the list until you come to the Video heading.
You'll see - PCI Express (PCI-E x16) slot available
This means you have a PCI Express x16 graphics slot on the motherboard, and it is open, and available.
You can use a PCI Express graphics card.
Two things I would like to note.
1) You need to check the System Requirements of the PCI Express graphics card you're going to buy, and see if your System Resources are able to support it.
The main thing you need to look for here, is what power is required for the graphics card.
Does your Power Supply have the necessary Wattage?
Not only does your Power Supply have to be able to deliver the necessary power for the computer system resources (Processor, Ram Memory, etc), it also has to be able to deliver enough power for THAT graphics card.
Since eMachines Support doesn't list the power of the Power Supply, I searched online for a Power Supply replacement for the C6535.
Seems the C6535 comes with a 300 Watt power supply.
Problem is, back in the day the C6535 was made, power supply manufacturers were 'Fudging' the true maximum Wattage, that their power supply's were truly able to deliver.
A more realistic figure, is 70 percent of the maximum rated Wattage stated.
This would be 210 Watts.
Therefore, you're going to need a better power supply, to support any of the really decent PCI Express graphics cards out there.
2) PCI Express came out in 2004.
PCI Express is a technology.
The PCI Express technology has gone through three major changes, or upgrades, since it came out.
A) PCI Express 1.0 version
B) PCI Express 1.1 version
C) PCI Express 2.0 version
PCI Express graphics cards now, are made in the PCI Express 2.0 version.
You can use a PCI Express 2.0 graphics card in a computer with PCI Express 1.1 technology.
PCI Express 2.0 is Backward Compatible with the PCI Express 1.1 technology.
Your computer uses the PCI Express 1.1 technology.
If you use a PCI Express 2.0 graphics card in a computer with PCI Express 1.1 technology, you won't get the full capability of the PCI Express 2.0 graphics card.
Will you notice?
We haven't begun to fully use all the bandwidth of the PCI Express 1.1 technology yet, much less PCI Express 2.0
(PCI Express 3.0 technology is just around the corner, and getting ready to be used on newer graphic cards. Marketing strategy)
Have any further questions concerning this, please post in a Comment.
Information on PCI Express,http://en.wikipedia.org/wiki/PCI_Express