draw angle of Inclination

Question

Καλημέρα!!

I 'm trying to draw a line with the angle of inclination, but nothing happens. What am I doing wrong?

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz,pgfplots}

\usetikzlibrary{calc,patterns,angles,quotes}

\begin{document}
    \begin{tikzpicture}[>=latex]
            \begin{axis}[
    ticks=none,
    axis x line=center,
    axis y line=center,
    xlabel={$x$},
    ylabel={$y$},
    xlabel style={below right},
    ylabel style={above left},
    xmin=-2,
    xmax=2,
    ymin=-0.5,
    ymax=3]
    \addplot [domain=-2:2,ultra thick] {2*x+1} node [pos=0.95, below left] {$C_f$};
    \coordinate (A) at (0,1);
    \coordinate (B) at (-0.5,0);
    \coordinate (C) at (5,0);
    \pic [draw, ->, "angle name", angle radius=1, angle eccentricity=1.5] {angle = C--B--A};
            \end{axis}

    \end{tikzpicture}
\end{document}

Answer 1

It is because you are running in the old compatibility mode. If you insist on this, you'd need to prepend axis cs: to your coordinates. However, I would like to argue that it is easier to switch to a newer version, which can be achieved by adding \pgfplotsset{compat=1.16}. (I also gave your angle the name \varphi, but of course you could go back to angle name.)

\documentclass{article}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=1.16}
\usetikzlibrary{calc,patterns,angles,quotes}

\begin{document}
    \begin{tikzpicture}[>=latex]
            \begin{axis}[
    ticks=none,
    axis x line=center,
    axis y line=center,
    xlabel={$x$},
    ylabel={$y$},
    xlabel style={below right},
    ylabel style={above left},
    xmin=-2,
    xmax=2,
    ymin=-0.5,
    ymax=3]
    \addplot [domain=-2:2,ultra thick] {2*x+1} node [pos=0.95, below left] {$C_f$};
    \coordinate (A) at (0,1);
    \coordinate (B) at (-0.5,0);
    \coordinate (C) at (5,0);
    \pic [draw, ->, "$\varphi$", angle radius=1cm, angle eccentricity=1.5] 
    {angle = C--B--A};
            \end{axis}

    \end{tikzpicture}
\end{document}

Answer 2

A PSTricks solution only for comparison purposes.

\documentclass[pstricks,border=1pt]{standalone}
\usepackage{pst-plot}
\begin{document}
\begin{pspicture}(-2,-1)(1.4,3.4)
\psaxes[ticks=none,labels=none]{->}(0,0)(-2,-1)(1,3)[$x$,0][$y$,90]
\psplot[algebraic]{-1.4}{.4}{2*x+2}
\psarc{->}(-1,0){.7}{0}{!2 1 atan}
\uput{.3}[!2 1 atan 2 div](-1,0){$\varphi$}
\end{pspicture}
\end{document}