What is the graphics card in an Emachines T3985 and is it DirectX 9.0 compatible?

Answer 1

That graphics card is an Intel® Extreme Graphics2 3D
64MB shared video memory.
http://www.e4me.com/support/product_support.html?cat=Desktops&subcat=T-Series&model=T3985

It supports DX7 and DX8.
http://www.intel.com/products/chipsets/eg2/index.htm

Answer 2

http://www.shopping.com/xPF-E-Machines-T3985

Your PC's motherboard uses the Intel 865GV chipset which has the Extreme Graphics 2 integrated graphics. It was designed during the DX8 era.
http://www.intel.com/products/chipsets/eg2/index.htm

Your graphics expansion option is also limited to the slow PCI bus since there is no true graphics (AGP or PCIe) expansion port on the motherboard. That motherboard was designed for budget business desktops and not for performance PC.