why the line x = 4 is a vertical line.

think of an equation as

"a story about the points on a certain line"

in this case it says, x = 4, no mention is made of y, so I guess y can be anything.

how about some points ?
(4,1), (4,2), (4,-5), (4,3456) .....

is the x always 4 ?

now plot those points, what will you get ?