\pgfplotsset{compat=1.14}

\newcommand{\tvalue}{1.0}

% Define the parameters t_1 and t_2
\newcommand{\tonevalue}{1.7}
\newcommand{\ttwovalue}{0.5}

% Calculate intersection point for the two lines
\pgfmathsetmacro{\xiValue}{(\tvalue - \ttwovalue) / (\tonevalue-\ttwovalue)}
\pgfmathsetmacro{\yiValue}{(\tonevalue)*\xiValue}


\begin{tikzpicture}
    \begin{axis}[
        xlabel={$\log_\delta \rho$},
        ylabel={$\log_{\frac{1}{\delta}}|E_\rho|$},
        ylabel style={sloped like x axis}, 
        xmin=0, xmax=1,                  
        ymin=0, ymax={\tvalue},         
        xtick={0, 1},                  
        ytick={0, \tvalue},           
        yticklabels={$0$, $t$},      
        axis lines=left,            
        width=0.45\textwidth,      
        height=0.45\textwidth,    
        clip=false,
    ]

    % Line from (0,0) to (xiValue, yiValue) with slope \tonevalue
    \addplot[
        dashed,
        color=myblue,
        thick
    ] coordinates {(0,0) (\xiValue, \yiValue)}
    node[pos=0.5, above, sloped, font=\footnotesize] {Slope $= t_1$}; 

    % Line from (xiValue, yiValue) to (1,t) with slope \ttwovalue
    \addplot[
        dashed,
        color=myblue,
        thick
    ] coordinates {(\xiValue, \yiValue) (1, \tvalue)}
    node[pos=0.5, above, sloped, font=\footnotesize] {Slope $= t_2$}; 
    \end{axis}
  \end{tikzpicture}
