Final answer:
The line denoted by the equation x=4 is a vertical line and is therefore parallel to the y-axis in a cartesian coordinate system.
Step-by-step explanation:
The equation x=4 describes a line that is vertical on a two-dimensional graph. In the cartesian coordinate system, which consists of a horizontal axis (the x-axis) and a vertical axis (the y-axis), a line like x=4 does not vary as y changes, meaning it is parallel to the y-axis. All points on this line have the same x-coordinate (which is 4), but the y-coordinate can be any number, illustrating that the line is a vertical one.
This contrasts with a horizontal line, which would have an equation like y=c, where c is some constant, and would be parallel to the x-axis because the y-coordinate does not change. The two axes themselves are mutually perpendicular to each other. Understanding that the coordinate system is based on perpendicular axes is key to identifying the relationships between equations of lines and the axes they are parallel to.