Step 2: The Basics

The X and Y Axis are lines, so they go on indefinitely, and most higher level Math looks at them as more of a "Plus" Sign. The Center Point, (0,0) is called the Origin. Not (0,0.01), not (0,0.00000001), exactly (0,0), were the two Axis cross.

There are four Quadrants in a Graph, and they start at the top right one, and move Counter/Anti-Clockwise. As you can see, they're named Quadrant I, Quadrant II, Quadrant III, and Quadrant IV. (Roman Numerals for 1,2,3,4). In Quadrant I, the X and Y are both positive numbers. In Quadrant II, the X is negative, and the Y is Positive. In Quadrant III, the X and the Y are negative. And in Quadrant IV, the X is positive, and the Y is not.
I like your explanations. I think that for demonstration purposes, an ink pen (fine point black marker) and a ruler would be great to use so your examples are clean and clear. Other than that, i think you did a great job.
I completely agree about the choice of pens or why not a softer and darker pencil, anyway you did a pretty good work
Now all you have to do is not skip the steps so that you won't get lost (to all those people who are only beginners in algebra)
Not bad, keep going though (graphing in 3 dimensions, graphing in polar, cylindrical, spherical coordinates)
It's hard to draw a 3-dimensional graph on a piece of paper (unless you roll it into a cone and say it's (x&sup2;+y&sup2;) = z&sup2;). In my experience graphing 3D involves computer programs or a good imagination.<br/>