Question: Strange issue - graphically solving e - problems graph breaks down

I was checking out a problem that graphically solved e (2.71828....) etc..

A procedure was created to find the slopes of incremental numbers between 2 selections.  The procedure was in it's simplest form like this

E := proc(c,d)
plot({(c+(d-c)*j/10^x-x-1 $ j=0..10}, x=0..(d-c)/1000,xtickmarks=0);
end;

Now so I start the process

E(2,3);

The slope closest to 0 and just under will determine my next decimal point.  So I find the next number as 7.  I continue finding more decimal points graphically using the procedure.

E(2.7,2.8);

E(2.71,2.72);

E(2.718,2.719);

E(2.7182,2.7183);

E(2.71828,2.71829);

Something funny starts to happen here, the lines aren't so straight anymore.  So I continue...

E(2.718281,2.718282);

All hell breaks loose and the graph has fallen apart.  Specifying numpoints to a higher value doesn't seem to work.  Can someone tell me what's happening here?