Question

What is the equation of the line through (4, -8) that is perpendicular to the line y = 8?

Answer 1

`x = 4`

Explanation:

A line that is defined by `y=8` mean that it is parallel to the x-axis (horizontal) and passes through the point `y=8 ->(x,y)=(0,8)`
This is true for any `x` that is in the set `-oo to +oo`

As this line is horizontal it has to mean that the line that is perpendicular is vertical. So it is parallel to the y-axis.

The vertical line must pass through the given point ( 4, -8). This means that the value of the `x` is 4 for any and all values of `y`. So the equation of a vertical line passing through the point ( 4, -8) is `x = 4`