matplotlib · kyracho · Aug 23, 2024 · Aug 23, 2024 · Aug 23, 2024 · Aug 23, 2024
diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
@@ -1499,6 +1499,9 @@ def get_transform(self):
         ax = self.axes
         points_transform = self._transform - ax.transData + ax.transScale
 
+        # Initialize the manual_slope variable to False
+        manual_slope = False
+
         if self._xy2 is not None:
             # two points were given
             (x1, y1), (x2, y2) = \
@@ -1517,10 +1520,13 @@ def get_transform(self):
             # one point and a slope were given
             x1, y1 = points_transform.transform(self._xy1)
             slope = self._slope
+            # Since the slope is provided manually, set manual_slope to True
+            manual_slope = True
         (vxlo, vylo), (vxhi, vyhi) = ax.transScale.transform(ax.viewLim)
+
         # General case: find intersections with view limits in either
         # direction, and draw between the middle two points.
-        if np.isclose(slope, 0):
+        if not manual_slope and (np.isclose(slope, 0, atol=1E-15) or slope == 0):
             start = vxlo, y1
             stop = vxhi, y1
         elif np.isinf(slope):

diff --git a/lib/matplotlib/tests/test_lines.py b/lib/matplotlib/tests/test_lines.py
@@ -436,3 +436,22 @@
     with pytest.raises(ValueError,
                        match="Cannot set a 'slope' value while 'xy2' is set"):
         line2.set_slope(3)
+
+
+def test_line_slope():
+    slopes_to_test = [1E-8, 1E-9, 1E-10, 1E-11, 1E-12, 1E-13]
+
+    for slope in slopes_to_test:
+        fig, ax = plt.subplots()
+        line = ax.axline(xy1=(0, 0), slope=slope)
+
+        # Extract the slope from the line's properties
+        calculated_slope = line.get_slope()
+
+        if calculated_slope == 0:
+            with pytest.raises(ValueError, match="line should not be horizontal"):
+                raise ValueError("line should not be horizontal")
+        else:
+            print(f"Slope {slope} correctly processed as {calculated_slope}")
+
+        plt.close(fig)  # Close the figure after each test to free up resources