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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.

y varies inversely as x and when x = 4, y = 2.

Learn how to solve an inverse variation problem where y varies inversely with x. Given the values x = 4 and y = 2, discover how to derive the equation y = 8/x. Suitable for students in Grades 7-9.

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