Yes, it is true; slope zero is no slope.
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A horizontal line has a slope of zero. The equation of a horizontal line is y = a.
Horizontal lines always have a slope of zero. (i.e completely flat, level surfaces have a slope of zero). However a line does not have to have a slope of zero in order to be a line.
zero is horizontal, undefined is vertical
a horizontal line - kinda
That line is horizontal on the graph. Its slope is zero.