There are just too many ways to answer this question.
Some basic background here, though info per se is not its intent. Other pages were too old in this ever-changing topic. http://www.extremetech.com/gaming/178276-valve-open-sources-its-directx-to-opengl-translation-software-here-come-the-steamos-and-linux-games
You're either wanting to evaluate a hardware purchase for running Linux, or wanting to run Windows-specific games or such. For hardware, you really want to look it up in hardware compatiblity guides; if you want to take the risk of just looking for "OpenGL" on the box, that's up to you.
If you're trying to get a particular piece of software to work, how it might be done is more specific to the software itself than most will admit. Looking in places dedicated to that software is usually the better idea, but if you want to continue here, no real help is possible without knowing some specifics of what you wish to do.
There are postings about "DirectX on Linux (wine)", etc, but you want the method specific to the target software. DirectX, or Direct3D, will not be ported to Linux or elsewhere. Its sole advantage is that it is native to Windows, thus driver API's supply its interfaces. Except for that, OpenGL (or Mesa3D) is at least "equivlent", if not better.
(Or yeah, what bigpaws said succinctly while I was looking for more characters to type