A vertical line is a line that goes straight up and down. We often think of a vertical line as being the opposite of a horizontal line.
In coordinate geometry, a vertical line is parallel to the y-axis on the coordinate plane. Below is the graph of a vertical line that has an x-intercept of (h, 0).
The vertical line is parallel to the y-axis, so it does not intersect it. Any vertical line does not intersect the y-axis unless the vertical line is the y-axis.
The x-coordinate for any point on the vertical line is h. The y-coordinate can be any real number (we say y is arbitrary).
The slope for a vertical line is undefined. Using the points (-4, 0) and (-4, 3) for the vertical line below, the slope is which is undefined since we can't divide by zero.
Since the slope is undefined for a vertical line, we can't use the slope-intercept form, y = mx + b, to write an equation for it. To find the equation of a vertical line having an x-intercept of (h, 0), use the standard form Ax + By = C where A = 1, B = 0, and C is the x-intercept, h. Substituting these values and simplifying the equation, we get, x = h and see that the equation is simply the x-coordinate for the x-intercept.