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\documentclass[margin=10pt]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{intersections}
\usepgfplotslibrary{fillbetween}
\begin{document}
		
	\begin{tikzpicture} 
	\begin{axis}[domain=0.125:220, samples=400, xmin=0, xmax=100, ymin=0, ymax=100, xlabel = $x~Achse$, ylabel = $y~Achse$]
	\path[name path=axisy] (axis cs:0,100) -- (axis cs:70,100);
	\path[name path=axisx] (axis cs:30,0.01) -- (axis cs:100,70);
	\addplot+[mark=none, name path=A] {\x+30} node[above, rotate=40] at (20,100) {$Instabil$} node[above, color= black, rotate=40] at (50,70) {$Stabil$};
	\addplot+[mark=none, name path=B] {\x-30} node[below, rotate=40] at (75,55) {$Instabil$};
	
	 \addplot [
	 thick,
	 color=blue,
	 fill=blue, 
	 fill opacity=0.05
	 ]
	 fill between[
	 of=A and axisy,
	 soft clip={domain=0:1},
	 ];
	\end{axis} 
	\end{tikzpicture}
\end{document}

\documentclass[margin=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}% <- immer compat setzen!
\usepgfplotslibrary{fillbetween}
\begin{document}
\begin{tikzpicture} 
\begin{axis}[
  domain=0:100,% geändert
  %samples=400,% für Geraden würde sogar samples=2 reichen
  xmin=0, xmax=100,
  ymin=0, ymax=100,
  xlabel = $x~Achse$, ylabel = $y~Achse$
]
\path[name path=axisy] (0,100) -- (100,100);
\path[name path=axisx] (0,0) -- (100,0);
\addplot+[mark=none, name path=A] {\x+30}
  node[above, rotate=40] at (20,70) {$Instabil$}
  node[above, color= black, rotate=40] at (50,40) {$Stabil$}
;
\addplot+[mark=none, name path=B] {\x-30} 
  node[below, rotate=40] at (75,20) {$Instabil$}
;

\addplot [blue,fill opacity=0.05]
  fill between[of=A and axisy]
;
\addplot [red,fill opacity=0.05]
  fill between[of=B and axisx]
;
\end{axis} 
\end{tikzpicture}
\end{document}