Horizontal lines are parallel to the horizon or parallel to level ground. They have a slope of zero and are parallel to the x-axis on a graph. Vertical lines are perpendicular to the horizon, parallel to the y-axis on a graph and have undefined slope.
The term "horizontal" derives from the Latin "horizontem" which means "flat." The term "vertical" derives from the Latin "vertex," which means "highest point."
The slope of a line refers to the change in the rise, or y-value, divided by the run, or the change in x-value. Because a horizontal line does not change in y-value with changes in x-value, its slope may be calculated as zero divided by any number. This results in a slope of zero. For vertical lines, the slope equation leads to a division by zero, which is undefined.