I want to make the selected line an exact number long, however, I don't see any way to do this. I have tried using the measure tool however its imprecise, and hard to work with. I have also tried looking in the transform menu however it only shows the measurements of the whole object
In your pictured example I would select the end vertex, grab it and use vertex snapping to put it on top of the next vertex to the right.
Without changing my selection I would now grab it again, lock movement to the Y axis and type in how long I want it to be (you may need to use a negative value if you are moving towards -Y).