Linear is simply moving forward or back in a straight line. Robbins is not just speaking of straight out sprints like the 40yd dash, he is speaking more toward variations of starting and stopping, speeds and distances. He speaks to two examples, the jog to sprint and the sprint to jog. Either method used is focused on the distance traveled. For example, you could jog for 30yds then sprint for 5yds, then jog for 30yds and sprint for 10yds. Each time you could increase your sprint or jog distance depending on what phase you are in or what goal you are looking for. The same methodology would hold true for the sprint to jog. The key point to remember with this method is that you want to feel and noticeable see a change in gears from the sprint to jog or vice versa.
We live in a world that is not just forward and back. You, especially live in a world that is full of multi-directions. They goal of this phase is to keep the drills simple so you can really focus on the acceleration and deceleration off each direction. The cahange in direction and speed will teach your body how to affectively navigate through hallways, backyards, buildings, etc. Indirectly it touches on agility, or your ability to change directions while still maintaining your speed. Below is a diagram of a mach set-up for this phase. It is intending to be run a number of reps at a time or be built up to that.
In this phase of development you are looking to focus on your specific work to rest ratio that your job requires. It may be the same across the board or it may be different from fire to police and military. They key is to find that specific ratio and utilize that in this phase. For example, if a firefighter typically worked while in a building or any situation for two minutes straight but then had five-six minutes of rest before asked to go again you would have a ratio of 3:1, 2 minutes of work and 6 minutes of rest. If you are really not sure what your ratio is, try looking at other activities that may require a similar work to rest ratio. Most are unique to their activity but you may find a similarity that works for you. My guess is you probably have a negative ratio, meaning you work more than you rest. If that is the case you would start with a small time frame like 10 seconds and only take a five second rest then go again for multiple bouts. Over time you can increase the work and rest time but still keeping it a negative ratio. So ultimately you could work up to a minute of work with only thirty seconds of rest. As long as the ratio stays consistent your number could go up to five minutes of work. That five minutes of work may sound little compared to what you do in the field, but remember that the intensity is constant and increased so it will make up for the difference.