A friend asked me this question:
The product of the gradient of any two lines perpendicular to each other is $-1$. Now, the lines $x=0$ and $y=0$ are perpendicular to each other. If you take the product of both their gradients, you dont get $-1$? Or do you? The question is missing on something fairly fundamental here as far as I think. Could you point it out and clear this problem? I have some ideas but I'm not writing them down because they might be too stupid.
By "gradient", I suppose you mean the slope of the line $y = f(x)$. If so, then notice that the line $x = 0$ cannot be properly written as a function of $x$, and so its gradient is not defined. That is, we don't have a change in $y$ over a change in $x$ because between any two points, the change in $x$ is $0$.