Ttgjyuk

I was wondering if there was a more succinct way to express the following plot (I'm using the plain format):

input tikz
tikzpicture
 draw[help lines, ystep=.5] (-.2,-10) grid (12.5,15);
 draw[->] (0, -10) to (0, 15) node[above] $y$;
 draw[->] (0, 0) to (12.5, 0) node[right] $x$;
 draw (1,-.5) node $1$;
 draw (2,-.5) node $2$;
 draw (3,-.5) node $3$;
 draw (4,-.5) node $4$;
 draw (5,-.5) node $5$;
 draw (6,-.5) node $6$;
 draw (7,-.5) node $7$;
 draw (8,-.5) node $8$;
 draw (9,-.5) node $9$;
 draw (10,-.5) node $10$;
 draw (11,-.5) node $11$;
 draw (12,-.5) node $12$;

 draw (-.5,-10) node $-20$;
 draw (-.5,-9) node $-18$;
 draw (-.5,-8) node $-16$;
 draw (-.5,-7) node $-14$;
 draw (-.5,-6) node $-12$;
 draw (-.5,-5) node $-10$;
 draw (-.5,-4) node $-8$;
 draw (-.5,-3) node $-6$;
 draw (-.5,-2) node $-4$;
 draw (-.5,-1) node $-2$;
 draw (-.5,0) node $0$;
 draw (-.5,1) node $2$;
 draw (-.5,2) node $4$;
 draw (-.5,3) node $6$;
 draw (-.5,4) node $8$;
 draw (-.5,5) node $10$;

 draw (0,-10) circle (2pt);
 draw (1,-9) circle (2pt);
 draw (2,-8) circle (2pt);
 draw (3,-7) circle (2pt);
 draw (4,-6) circle (2pt);
 draw (5,-5) circle (2pt);
 draw (6,-4) circle (2pt);
 draw (7,-3) circle (2pt);
 draw (8,-2) circle (2pt);
 draw (9,-1) circle (2pt);
 draw (10,0) circle (2pt);
 draw (11,1) circle (2pt);
 draw (12,2) circle (2pt);
endtikzpicture
bye

It comes out so big it doesn't fit on a page.

Here's a LaTeX version.

documentclass[tikz,border=3.14mm]standalone
usepackagetikz
begindocument
begintikzpicture
 draw[help lines, ystep=.5] (-.2,-10) grid (12.5,15);
 draw[->] (0, -10) to (0, 15) node[above] $y$;
 draw[->] (0, 0) to (12.5, 0) node[right] $x$;
 foreach X in 0,...,12
 ifnumX>0
 node at (X,-0.5) $X$;
 fi
 draw (X,-10+X) circle (2pt); 
 foreach Y in -20,-18,...,10
 node at (-0.5,Y/2) $Y$;
endtikzpicture
enddocument

Amazingly the following does run through with pdftex

input tikz
tikzpicture
draw[help lines, ystep=.5] (-.2,-10) grid (12.5,15);
 draw[->] (0, -10) to (0, 15) node[above] $y$;
 draw[->] (0, 0) to (12.5, 0) node[right] $x$;
 foreach X in 0,...,12
 ifnumX>0
 node at (X,-0.5) $X$;
 fi
 draw (X,-10+X) circle (2pt); 
 foreach Y in -20,-18,...,10
 node at (-0.5,Y/2) $Y$;
endtikzpicture
bye

So after spending a night reading the manual while in a trial-error-loop, after many solemn utterances to invoke supernatural power to inflict harm or punishment on something, all of which now regretted, I finally – victoriously – formed the following:

documentclassarticle
usepackagetikz
usetikzlibrarydatavisualization, datavisualization.formats.functions
begindocument
begintikzpicture
 datavisualization[
 school book axes
 , x axis=unit length=5mm
 , y axis=
 unit length=5mm
 , ticks=step=2
 , grid
 , scaling = min at 0cm and max at 5cm
 
 , visualize as line
 ]
 data[format=function] 
 var x : interval [0:12];
 func y = (value x - 10) * 2;
 ;
endtikzpicture
enddocument

Boom! Pow! Shazam! Holy function data format, Batman! This is pretty darn nice, it has to be said.

Only trouble I found, is that it does not work with the plain format, forcing the user to descend to a lower plane of enlightenment.