The problem of being parallel to $\mathbf y$ axis and undefined slope We all know the general equation for line $d$ is:
$d:y=ax+b$
I want you to suppose $d$ is parallel to $y$ axis.
Now , if we rearrange our equation , $x $will be equal to:
$$x=\frac{-b}{a}$$
It is clear that $a$ is undefined as line$d$ is parallel to $y$axis.But how $x$is equal to $-b$ over undefined?

"the general equation for line $d$ is: $d:y=ax+b$" This is not accurate. That's the general equation for a linear function, meaning that for each value of $x$ we get a unique value of $y$. This means that it specifically does not describe vertical lines, since for vertical lines there is only a single value of $x$ which works, and for that $x$-value there are infinitely many values for $y$.
A general equation for a line in the plane is
$$
ax + by = c
$$
where $a$ and $b$ are not both equal to $0$.
