Question

Find the equation of the line perpendicular to y=−2 that passes through the point (4, −2).

Answer 1

x = 4

because it is perpendicular, the new equation has to be a vertical since the original was horizontal. We know that it passes through (4,-2) so it has to be x=4

Answer 2

`x = 4`

Explanation:

the line

`y=-2`

is a horizontal line on the -2 of the y-axis (for any x value, the y value is always -2).

Thus since
`y=-2` is a horizontal line, a perpendicular line to a horizontal line has to be a vertical line.

Now, we want this vertical to pass through the point:

`(4,-2)`.

This means that the only option we have is the line:

`x=4`

because this is the equation of a vertical line sitting on the x = 4.

This can be better visualized in the attached image. where the red line is
`y = -2` and the dotted blue line is
`x = 4`