In coordinate geometry, a horizontal line is parallel to the x-axis on the coordinate plane. Below is the graph of a vertical line that has a y-intercept of (0, k).
The horizontal line is parallel to the x-axis so, it does not intersect it. Any horizontal line does not intersect the x-axis unless the horizontal line is the x-axis.
The y-coordinate for any point on the vertical line is k. The x-coordinate can be any real number (we say x is arbitrary).
The slope for a horizontal line is zero. Using the points (0, -4) and (3, -4) for the horizontal line below, the slope is:
Since the slope is zero for a horizontal line, we can use the slope-intercept form, y = mx + b to write an equation for it. Since m = 0, it becomes y = b.