The graph of inversely proportional relationships

Question

If y is inversely proportional to x, the graph of y against 1/x is a straight line through the origin. What i don't understand is as the line passes the origin, the value of y is 0, then the value of 1/x is also 0, then what is the value of x?

Answer 1

You wrote that "the graph of $y$ against $\frac{1}{x}$ is a straight line through the origin." That is not correct. The graph of $y$ against $\frac{1}{x}$ is indeed straight, but it doesn't include the origin point $(0, 0)$. So the premise of the question is wrong and the trouble you are concerned about doesn't arise.

Answer 2

$y$ is said to be inversely proportional to $x$ if whenever $$y = \frac{k}{x} \qquad \text{for all } x \neq 0$$ where $k$ is a constant.

I think the issue you are encountering is that when $x = 0$, the above is undefined. For example, when $k = 1$, we have