Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
the line
[tex]y=-2[/tex]
is a horizontal line on the -2 of the y-axis (for any x value, the y value is always -2).
Thus since [tex]y=-2[/tex] 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:
[tex](4,-2)[/tex].
This means that the only option we have is the line:
[tex]x=4[/tex]
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[tex]y = -2[/tex] and the dotted blue line is [tex]x = 4[/tex]
