The test does not do anything. get_slope just returns the value passed in. We cannot test the change by retrieving any AxLine properties because the change only affects the transform.

A test that would discriminate the change is

def test_axline_small_slope():
    """Test that small slopes are not coerced to zero in the transform."""
    line = plt.axline((0, 0), slope=1e-15)
    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 < 1e-13

It could be that you have to make the slope slightly larger 1e-15 is very close to the numerical limit and it may be that there we get to no change through the transform due to numerical precision.
Also you may need to change the limit assert dy < 1e-14. We can choose this empirically. I've not thought the transform stack through to find out what the expected dy for the given points is.

Probably we should add this, even though I wouldn't have added such a test in the first place when writing the function because not coercing small slopes would be the canonical implementation behavior.

Hi Tim,

I tested with slopes of 1e-15, 1e-14, and 1e-13, and I found that 1e-14 struck a good balance between being small enough to test the original issue and large enough to avoid potential floating-point precision issues.

For dy, I set the limit to 4e-12 because the test fails around 3.84e-12. This threshold ensures that the slope is not coerced to zero while allowing some margin for minor floating-point variations during transformation.

For example, with a slope of 1e-14, the expected dy is about 3.84e-12, and for a slope of 1e-13, it increases to around 3.84e-11. However, for very small slopes like 1e-15, floating-point precision limitations cause a slight deviation, resulting in a slightly higher dy (around 3.98e-13), breaking the linear progression.

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, confirming the slope is not coerced to zero
    dy = p2[1] - p1[1]
    assert dy > 0  
    assert dy < 4e-12  

Does this version look good to you for final integration? Let me know if you have any suggestions.

Thanks!