Determine the equation of a line perpendicular to the X-axis that passes through the point (4,1).

Answer 1

The equation for the x-axis is y = 0, as all points on the x-axis have a y-value of 0. A horizontal line that runs through, say, (4,1) would have an equation of y = 1 and be parallel to the x-axis.

A line perpendicular to the x-axis would have the opposite. The y-axis, for example, has an equation of x = 0 because any point on the y-axis has a y-value of 0.

Therefore, the equation of your vertical line passing through (4,1) is x = 4. Any other point on that line has an x-value of 4.

Answer 2

Perpendicular to the x-axis means

x = constant.

The equation is

x = 4