The problem states that $y$ varies inversely as $x$, and when $x = 4$, $y = 2$.

In general, if $y$ varies inversely as $x$, the relationship is described by the equation:

$y = \frac{k}{x}$

where $k$ is a constant.

To find the value of $k$, we can substitute the given values $x = 4$ and $y = 2$ into the equation:

$2 = \frac{k}{4}$

Multiplying both sides by 4:

$k = 8$

Thus, the equation describing the relationship between $y$ and $x$ is:

$y = \frac{8}{x}$

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What happens to $y$ when $x = 8$?
2. How would you describe the behavior of $y$ as $x$ approaches 0?
3. Can you express $x$ in terms of $y$ from the equation $y = \frac{8}{x}$?
4. What is the value of $y$ when $x = 2$?
5. How would you modify the equation if $y$ varied directly with $x$?

Tip: Inverse variation means that as one variable increases, the other decreases proportionally.