How to specify Latex graph scale

Question

I have had this issue for long and no solution yet despite my numerous research. I wish to know if it is possible to specify the axis scale in Latex graph as we normally do in Maths.

For Example I wish to specify "2 cm for 1 unit on the x-axis and 4 cm for 1 unit on the y-axis". I have the current code as shown below

    \begin{tikzpicture}[scale=2,dot/.style 2 args={circle,inner 
    sep=1pt,fill,label={#2:#1},name=#1}, extended line/.style={shorten >=- 
    #1,shorten <=-#1,draw=Cerulean}, extended line/.default=1cm]
    \begin{axis}[
      width=20cm,
      height=20cm,
      xmax=10,xmin=-10,
      ymin=-10,ymax=10,
      xlabel=$x$,ylabel=$y$,
      xtick={-10,...,10},
      ytick={-10,...,10},
      %domain=-7.5:10.5,
      axis lines=center, % default is to make a box around the axis
      x label style={at={(axis description cs:1,0.15)},anchor=west},
      y label style={at={(axis description cs:0.5,1.05)},anchor=north},
      width=10cm,
      height=11cm,
      grid=both,
      grid style={line width=.3pt, draw=gray!50},
      major grid style={line width=.5pt,draw=gray!90},
      minor tick num=4,
      enlargelimits={abs=0.5}
     ]
   \end{axis}
   \end{tikzpicture}

As you can notice, when compiled the axis numbering are so close to each other. I want to skip some. Thank you

Answer 1

The original question can be answered by set e.g. x=2cm. However, the last part of the question is a bit different. If you want to keep xmax=10,xmin=-10, and set the width (you specify it twice, once width=20cm and once width=10cm, the last key "wins"), then one can infer the unit length on the plot from this data. Your last question, however, sounds as the request to have the ticks less crowded. They are crowded because you set

  xtick={-10,...,10},

To have them less crowded you can either set

  xtick={-10,-8,...,10},

say, or do not specify them and set xtick distance=2, say. The analogous statements apply to y (and z in 3d plots).

\documentclass[dvipsnames,tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}%<- use a smaller version if you have an older installation

\begin{document}
    \begin{tikzpicture}[scale=2,dot/.style 2 args={circle,inner 
    sep=1pt,fill,label={#2:#1},name=#1}, extended line/.style={shorten >=- 
    #1,shorten <=-#1,draw=Cerulean}, extended line/.default=1cm]
    \begin{axis}[
      %width=20cm,
      %height=20cm,
      xmax=10,xmin=-10,
      ymin=-10,ymax=10,
      xlabel=$x$,ylabel=$y$,
      %xtick={-10,-8,...,10},
      %ytick={-10,-8,...,10},
      %domain=-7.5:10.5,
      axis lines=center, % default is to make a box around the axis
      x label style={at={(axis description cs:1,0.15)},anchor=west},
      y label style={at={(axis description cs:0.5,1.05)},anchor=north},
      width=10cm,
      height=11cm,
      grid=both,
      grid style={line width=.3pt, draw=gray!50},
      major grid style={line width=.5pt,draw=gray!90},
      minor tick num=4,
      enlargelimits={abs=0.5},
      xtick distance=2,ytick distance=2,
     ]
   \end{axis}
   \end{tikzpicture}
\end{document}

I am posting this also to inform you about the way we exchange codes here. As stated by Alessandro Cuttin, you are supposed to post a complete example. The above code is such an example.