# How to draw a filled irregular graphics only using tikz in beamer

I am very new to Beamer and tikz. I want to draw an irregular graphics for my presentation as attached. I think it should be pretty simple but I just don't know how to draw it. To make simple, please only use tikz (and matrix) and don't use other library. Many thanks!!!

\documentclass[border=0.5cm]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
% \draw [help lines] (0,0) grid (15,15);
\draw [fill=gray!20] plot [mark=none, smooth cycle] coordinates {(-5.97,4.742) (-2.554,5.713) (0.393,5.929) (4.295,4.291) (7.312,0.891) (6.7,7.668) (4.264,10.821) (0.948,10.904) (-5.973,5.294)};
\draw [thick,-latex] (-11.5,0) -- (11.5,0) node [right,scale=3] {$u$};
\draw [thick,-latex] (0,-5) -- (0,11) node [above,scale=3] {$t$};
\draw [dashed] (0,4.65) -- + (-8,0);
\draw [thick] (-8,3.5) -- + (-10:18);
\node [scale=3] at (-11.5,3.5) {$\lambda u+t=g(\lambda)$};
\coordinate (g) at (0,2.1);
\fill (g) circle (3.5pt) node [right,scale=3] {$g(\lambda)$};
\coordinate (p) at (0,4.65);
\fill (p) circle (3.5pt) node [right,scale=3] {$p^{*}$};
\end{tikzpicture}
\end{document}