A horizontal line is side-to-side like the horizon of the Earth:
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...not vertical, which is up and down:
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if the slope is 0, the line is horizontal.
The slope of a horizontal line is zero.
The straight level line is said to be horizontal.
A line which divides a body into two parts, such that each part is the mirror image of the others, then the line is called a line of symmetry. If such a line is parallel to the horizontal plane, then it is called a horizontal line of symmetry. Else, if the line of symmetry is perpendicular to the horizontal plane then it is a vertical line of symmetry.
Horizontal lines have a slope of 0.