The concept of linear playing is classically derived. Back in the 1950's, composers gave rise to the concept of 'pointillism', where orchestral instruments were played one-after-the-other in order to create a linearly distributed origin of sound.
In drumming terms, the concept revolves around each limb striking a different part of the kit at different times and never at the same time.
There are two patterns I'm going to demonstrate here - a more basic example of this linear pattern, played at 105bpm, with just normal velocity hits and accents on the snare, as transcribed here:

I have also written out the second pattern, which is what you should use the first pattern to develop towards, uses both ghost notes and accents, and is played at 135 bpm:

Note the difference in notation in the second example.
I recommend practicing these to a click-track - surprisingly difficult with linear beats!
Here is a video demonstration: