The "origin" of a line is simply the points (0, 0)
To draw a line that passes through the origin (0, 0) & has a slope of 3/5, we simply start by drawing a point at (0, 0).
Then, from there, you use the slope to find your next points.
Slope = rise/run
So, 3 is the rise, and 5 is the run.
So, starting from (0, 0), you go up 3 times, and go to the right 5 times. So, (3, 5) is your next point. Just continue doing that and you'll get a line.
~Hope I helped!~