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This problem involves direct proportionality, meaning \( y \) is directly proportional to \( x \), or:

\[
y = kx
\]

where \( k \) is the constant of proportionality.

We are given that when \( x = 512 \), \( y = 128 \). To find \( k \), we can plug these values into the equation:

\[
128 = k \times 512
\]

Solving for \( k \):

\[
k = \frac{128}{512} = \frac{1}{4}
\]

Now that we know \( k = \frac{1}{4} \), we can use this value to find \( y \) when \( x = 64 \):

\[
y = \frac{1}{4} \times 64 = 16
\]

Thus, the value of \( y \) when \( x = 64 \) is \( \boxed{16} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What would the value of \( y \) be if \( x = 256 \)?
2. How does inverse proportionality differ from direct proportionality?
3. Can the constant \( k \) ever be negative in direct proportionality?
4. How would you solve for \( y \) if the relationship were \( y = kx^2 \) instead?
5. What is the effect on \( y \) if \( x \) is halved in a direct proportional relationship?

**Tip:** In any proportional relationship, always start by finding the constant of proportionality \( k \).

The value of y is directly proportional to the value of x. When x = 512, y = 128. What is the value of y when x = 64?

In this problem, solve for y using the direct proportionality formula y = kx. Given x = 512 and y = 128, find the constant of proportionality and calculate y when x = 64. Suitable for Grades 6-8.

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