diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
index 1203862a3f50..0b7ff7600eb3 100644
--- a/lib/matplotlib/lines.py
+++ b/lib/matplotlib/lines.py
@@ -1,6 +1,5 @@
 """
-The 2D line class which can draw with a variety of line styles, markers and
-colors.
+2D lines with support for a variety of line styles, markers, colors, etc.
 """
 
 from numbers import Integral, Number, Real
@@ -715,26 +714,16 @@ def _transform_path(self, subslice=None):
         self._transformed_path = TransformedPath(_path, self.get_transform())
 
     def _get_transformed_path(self):
-        """
-        Return the :class:`~matplotlib.transforms.TransformedPath` instance
-        of this line.
-        """
+        """Return this line's `~matplotlib.transforms.TransformedPath`."""
         if self._transformed_path is None:
             self._transform_path()
         return self._transformed_path
 
     def set_transform(self, t):
-        """
-        Set the Transformation instance used by this artist.
-
-        Parameters
-        ----------
-        t : `matplotlib.transforms.Transform`
-        """
-        super().set_transform(t)
+        # docstring inherited
         self._invalidx = True
         self._invalidy = True
-        self.stale = True
+        super().set_transform(t)
 
     def _is_sorted(self, x):
         """Return whether x is sorted in ascending order."""
@@ -1014,10 +1003,7 @@ def get_ydata(self, orig=True):
         return self._y
 
     def get_path(self):
-        """
-        Return the :class:`~matplotlib.path.Path` object associated
-        with this line.
-        """
+        """Return the `~matplotlib.path.Path` associated with this line."""
         if self._invalidy or self._invalidx:
             self.recache()
         return self._path
@@ -1477,9 +1463,8 @@ def draw(self, renderer):
 
 class VertexSelector:
     """
-    Manage the callbacks to maintain a list of selected vertices for
-    `.Line2D`. Derived classes should override
-    :meth:`~matplotlib.lines.VertexSelector.process_selected` to do
+    Manage the callbacks to maintain a list of selected vertices for `.Line2D`.
+    Derived classes should override the `process_selected` method to do
     something with the picks.
 
     Here is an example which highlights the selected verts with red
@@ -1508,9 +1493,8 @@ def process_selected(self, ind, xs, ys):
     """
     def __init__(self, line):
         """
-        Initialize the class with a `.Line2D` instance.  The line should
-        already be added to some :class:`matplotlib.axes.Axes` instance and
-        should have the picker property set.
+        Initialize the class with a `.Line2D`.  The line should already be
+        added to an `~.axes.Axes` and should have the picker property set.
         """
         if line.axes is None:
             raise RuntimeError('You must first add the line to the Axes')
@@ -1528,8 +1512,7 @@ def __init__(self, line):
 
     def process_selected(self, ind, xs, ys):
         """
-        Default "do nothing" implementation of the
-        :meth:`process_selected` method.
+        Default "do nothing" implementation of the `process_selected` method.
 
         Parameters
         ----------
@@ -1556,7 +1539,4 @@ def onpick(self, event):
 fillStyles = MarkerStyle.fillstyles
 
 docstring.interpd.update(Line2D_kwdoc=artist.kwdoc(Line2D))
-
-# You can not set the docstring of an instancemethod,
-# but you can on the underlying function.  Go figure.
 docstring.interpd(Line2D.__init__)