diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
index 72e74f4eb9c5..569669f76e8d 100644
--- a/lib/matplotlib/lines.py
+++ b/lib/matplotlib/lines.py
@@ -1520,7 +1520,7 @@ def get_transform(self):
         (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 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
index 531237b2ba28..902b7aa2c02d 100644
--- a/lib/matplotlib/tests/test_lines.py
+++ b/lib/matplotlib/tests/test_lines.py
@@ -436,3 +436,14 @@ def test_axline_setters():
     with pytest.raises(ValueError,
                        match="Cannot set a 'slope' value while 'xy2' is set"):
         line2.set_slope(3)
+
+
+def test_axline_small_slope():
+    """Test that small slopes are not coerced to zero in the transform."""
+    line = plt.axline((0, 0), slope=1e-14)
+    p1 = line.get_transform().transform_point((0, 0))
+    p2 = line.get_transform().transform_point((1, 1))
+    # y-values must be slightly different
+    dy = p2[1] - p1[1]
+    assert dy > 0
+    assert dy < 4e-12