Why is the line x=4 a vertical line?

Hi:

The equation x=4 refers to all ordered pairs whose x value is 4. Thus, for example, (4,o), (4,1), (4,2), etc. all satisfy the given equation. Notice that the three ordered pairs above fall on the vertical line passing through 4 on the x-axis. Indeed, all ordered pairs on such vertical line have x coordinate =4.

Regards,

Rich B.

Thanks a million!

The line x=4 is a vertical line because it is parallel to the y-axis. It can also be thought of as a line that passes through all points on the plane where x equals 4. To understand why it is vertical, let's go through the steps:

1. Recall that the equation of a line in the standard form is written as y = mx + b, where m is the slope and b is the y-intercept.
2. In this case, x=4 does not have a "y" term, which means that the slope (m) is undefined.
3. An undefined slope indicates that the line is vertical since a vertical line does not have a change in y-value for any given x-value.
4. By fixing x at a specific value of 4, the line x=4 will pass through all the points where x equals 4, forming a vertical line.

So, the equation x=4 represents a vertical line because it has no y-component and all the y-values can vary while x remains constant at 4.