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?
 A: "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 $0$.
A: By explicit equation we can’t describe lines parallel to $y$ axis. Indeed in the explicit form 
$$y=mx+n$$
$m$ represents the angular coefficient which $\to \infty$ for a vertical line thus this case can’t be described in such way.
For the general case we can refer to the implicit form
$$ax+by+c=0$$
which always holds.
A: What is the meaning of slope of a line? This means take two points on the line where $x$ co-ordinates differ by 1, and see how much the $y$ co-ordinates differ for those two points.
For example, if $(3,7)$ and $(4,23)$ are two points on the line the difference $23-7=16$ is the slope of the line connecting them.
In the case of a line parallel to the $y$-axis all the points have the same $x$ co-ordinate.  So slope is undefined. The equation is $x=c$, the constant value of $x$-coordinate.
