Since every point on the y-axis has 0 as its x-coordinate,
for example (0,5), (0,-4), (0,10), (0,1), (0,-100), (0,10000)
all have their x coordinates as 0.
Therefore the equation of the y-axis is simply a statement
that tells what x is for every point on the y-axis:
x = 0
Since the y-axis is a vertical line and vertical lines are
steeper than any other kind of line, no matter how large
their slope, and since there is no number larger than all
other numbers, the slope cannot be defined, so the y-axis
does not have a slope.
Edwin