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?

Group of answer choices

32

8

16

256

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

\[
y = kx
\]

where \( k \) is the constant of proportionality. First, we need to find \( k \) using the given values \( x = 512 \) and \( y = 128 \).

\[
128 = k \times 512
\]

Solving for \( k \):

\[
k = \frac{128}{512} = \frac{1}{4} = 0.25
\]

Now, using this constant \( k = 0.25 \), we can find \( y \) when \( x = 64 \):

\[
y = 0.25 \times 64 = 16
\]

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

The correct answer is:

**16**

Would you like more details or have any questions? Here are five related questions:

1. What happens to \( y \) if \( x \) is halved in a direct proportional relationship?
2. How would the equation change if \( y \) was inversely proportional to \( x \)?
3. What is the constant of proportionality in the context of this problem?
4. How can you verify the proportionality relationship with different values?
5. How does the graph of a direct proportional relationship look?

**Tip:** When dealing with direct proportionality, remember that as one variable increases, the other increases at a constant rate defined by the proportionality 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?

Learn how to solve direct proportionality problems with the equation y = kx. When x = 512, y = 128, find the value of y when x = 64. Understand how to calculate the constant of proportionality and apply it to solve for y. Suitable for students in Grades 6-8.

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