Labeling a slant asymptote

Question

I am using TikZ and pgfplots for the first time. (I am using it so that I can send class notes to students in a Calculus class that I am teaching.) I have a graph with a slant asymptote. Before I can use pgfplots for the graph, I have some adjustments needed for just the lines in the graph!

I saw in another post that shorten <=2ex, shorten >=2ex would shorten a line at each end by 2ex. This command shortened the vertical line but not the slanted line. I want arrowheads on both lines; they are on the vertical line but not the slanted line. I want the lines labeled in the same direction as the lines ... but off the line. So, I need to move one label up and one label to the right. Since arctan(3/2) = 56.31 degrees, I used rotate=56.31 in the options for the node. Is there a "slant" command for drawing such labels in the same direction as the line? One more thing. The label "y" for the y-axis is too close to the vertical line x=3/2. How do I adjust its position? (I don't like the position of the "x" for the x-axis, too.)

\documentclass{amsart}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}    

\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={\empty},ytick={\empty},
]

\draw[dashed,latex-latex,shorten <=2ex, shorten >=2ex] (-13,-17) -- (13,22) node[right,rotate=56.31,pos=0.1]{$\scriptstyle{y=(3/2)x+5/2}$};
\draw[dashed,latex-latex,shorten <=2ex, shorten >=2ex] ({1.5,0} |- {{axis description cs:1,1}}) -- ({{1.5,0}} |- {{axis description cs:1,-1}}) node[right,rotate=90,pos=0.5]{$\scriptstyle{x=3/2}$};
\end{axis}
\end{tikzpicture}

\end{document}

Answer 1

The reason why the shorten commands don't seem to work reliably is because you can't see the ends of your lines: they're outside the plot area, and are clipped off. To see the full lines, add clip=false to your axis options.

I would approach this differently: instead of using \draw commands, you can use "real" plots with the \addplot command. That way, you can specify the equations directly, instead of having to calculate the angle for the rotation beforehand.

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}    

\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
clip=false,
    axis lines=middle,
    xmin=-15,xmax=15,
    domain=-15:15, samples=50,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={\empty},ytick={\empty},
]

\addplot [dashed, latex-latex] {(3/2)*x+5/2} node [pos=0.25, anchor=south, font=\footnotesize, sloped] {$y=(3/2)x+5/2$};
\addplot [dashed, latex-latex] (1.5,x) node [pos=0.25, anchor=north, font=\footnotesize, sloped] {$x=3/2$};
\end{axis}
\end{tikzpicture}

\end{document}

Answer 2

You can use the sloped option instead of computing the angle:

Notes:

• I also replaced the slat fractions with a \frac as I think that looks much better.
• To get the axis labels at the tips you can use the Axis Labels At Tip style that I extracted from How to properly scale a TikZ/PGF picture which has a `\begin{axis}...\end{axis}`.
• The reason why there were not arrowheads on both ends can be seen if you set clip=false. The lines were way beyond the displayed range. So you can either edit the coordinates to get the end points of the lines into range or just increase the amount you shorten the line with. In the MWE below I increased the shorten amounts as that was simpler than computing appropriate coordinates to maintain the same slope and position.

Code:

\documentclass{amsart}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

%% https://tex.stackexchange.com/questions/17438/how-to-properly-scale-a-tikz-pgf-picture-which-has-a-beginaxis-endaxis
%%
\pgfkeys{/pgfplots/Axis Labels At Tip/.style={
        xlabel style={
            at={(current axis.right of origin)}, 
            xshift=1.5ex, anchor=center
        },
        ylabel style={
            at={(current axis.above origin)}, 
            yshift=1.5ex, anchor=center
        }
    }
}

\begin{document}    

\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
%    xtick={\empty},ytick={\empty},
    Axis Labels At Tip,
    %clip=false
]

\draw[dashed,latex-latex,shorten <=4ex, shorten >=15ex] (axis cs: -13,-17) -- (axis cs: 13,22) node[right,sloped, above,pos=0.15]{$y=\frac{3}{2}x+ \frac{5}{2} $};
\draw[dashed,latex-latex,shorten <=2ex, shorten >=2ex] ({1.5,0} |- {{axis description cs:1,1}}) -- ({{1.5,0}} |- {{axis description cs:1,0}}) node[right,rotate=90, below, pos=0.65]{$x= \frac{3}{2}$};
\end{axis}
\end{tikzpicture}

\end{document}