Let suppose that $R(x_1, y_1)$ is a point on the (x, y)plane and a line $L$ with slope $m$ passes through this point. There is a point $S(x_1, y_1)$ on $L$ such that $R$ and $S$ are coincident points. Then the point-slope equation can be given as:
$y_1-y_1 = m(x_1-x_1)$
If we don't know the value of $m$ then we do as follows:
$m = \frac {y_1-y_1} {x_1-x_1}$
$m = \frac 00$
But the division by $0$ is undefined. So I think it implies that for a point slope equation two points must not be coincident or their $x$ and $y$ coordinates must not be the same. Well, it is only my thinking, is there any condition like this in reality for a point slope equation?
If $R$ and $S$ are coincident, the line through them is not defined. A line can have any slope and go though that point. This is what causes your division by zero.
You can certainly form the point-slope equation with just one point if you are given the slope. If you are not given the slope it takes a second point to determine it.