Question

Why is the graph of an inverse of a function flipped over the line y = x instead of another line

Answer 1

Okay.
An inverse function says that we switch x & y values
f(x) = x
Instead x = y ...
Which means that the old x has a new value of y and the old y now has the value of x.
Flipping the function over the line y = x has that effect of switching the values (you can prove that to yourself :D)