The equation y= 4x + 1 is in the "slopeintercept" form of y=mx+b, where m is the slope (rise over run), and b is the yintercept (where the line will cross the vertical yaxis).
You need graph paper for an accurate graph (but it's possible to do it on notebook paper).
It's best to start at the yintercept and plot your first point there. Put a dot on the yaxis 1 unit up from the origin.
I like to rewrite the slope as a fraction, to better visualize the "rise over run" so 4 becomes 4/1. This means I rise negative 4 (fall 4) and run to the right 1.
So, starting at the dot you made at the yintercept, count down 4 units, then right 1 unit, and draw your second dot. You can repeat the process starting there for more points: count down 4, then right 1.
Lastly, you can go back to the yintercept and count in the opposite direction, since your slope is also equal to positive 4 over negative 1. You can then count UP 4 units, and LEFT 1 unit.
10/13/2013

Charles B.