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?
A.256
B.32
C.16
D.8

Given that \( y \) is directly proportional to \( x \), we can express this relationship as:

\[
y = kx
\]

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

### Step 1: Find the constant \( k \)
Using the values \( x = 512 \) and \( y = 128 \):

\[
128 = k \times 512
\]

Solve for \( k \):

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

### Step 2: Use the constant to find \( y \) when \( x = 64 \)

Now that we know \( k = \frac{1}{4} \), substitute \( x = 64 \) into the equation \( y = kx \):

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

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

The correct answer is **C. 16**.

Would you like further clarification or more details on this? 

Here are 5 related questions to expand this topic:
1. What happens to \( y \) if \( x \) is halved in a direct proportion?
2. How do you solve problems involving inverse proportionality?
3. Can a direct proportionality equation include additional constants?
4. What are some real-life applications of direct proportionality?
5. How does direct proportionality differ from linear functions?

**Tip:** In direct proportionality, as one variable increases, the other increases at the same rate, keeping the ratio between them constant.

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? A. 256 B. 32 C. 16 D. 8

Explore how to solve a direct proportion problem where y is directly proportional to x. Given that when x = 512, y = 128, find the value of y when x = 64. This example covers the key concept of direct proportionality, algebraic manipulation, and is suitable for students in Grades 6-8.

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