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Parallel to y-1=0 with y-intercept (0,-1)
This is a special case. Any time you have y=k, where k is a real number and there's no x, you have a horizontal line going through k. In this case y=1 is a horizontal line going through y=1. Horizontal lines have slopes of 0 because y never changes.
A line parallel to a horizontal line would also be parallel. Horizontal lines have the same y value for every point.
The equation of a horizontal line going through (0,-1) is