Question

Write an equation of the line perpendicular to the line $x=2$ and passing through the point $(2,-8)$

Answer 1

$x=2$ is a vertical line.

Since, one vertical line is parallel to another horizontal line, therefore for the point $(2,-8)$,

The $y$-coordinate of every point on the graph is $-8$.

Furthermore if a point in the plane is not on the graph then its $y$-coordinate is not $-8$.

Therefore, a point $(x,y)$ in the plane is on the graph if and only is $y=-8$.

Hence, the equation of the line is $y=-8$.