y varies directly as x and y = 32 when x = 4. Find the constant of variation.

A. 8

B. 28

C. 36

D. 128

To find the constant of variation \( k \) for the direct variation \( y = kx \), we can use the values given: \( y = 32 \) when \( x = 4 \).

Substituting these values into the equation:

\[
32 = k \cdot 4
\]

Solving for \( k \):

\[
k = \frac{32}{4} = 8
\]

So the constant of variation is **A. 8**.

Would you like further details or have any questions? Here are some related questions you might consider:

1. How would you express the relationship between \( y \) and \( x \) using the constant of variation?
2. What would happen to \( y \) if \( x \) doubled?
3. Can you provide another example of direct variation?
4. How does this concept apply in real-life scenarios?
5. What is the difference between direct variation and inverse variation? 

**Tip:** Always remember that in direct variation, the ratio \( \frac{y}{x} \) remains constant.

y varies directly as x and y = 32 when x = 4. Find the constant of variation.

Discover how to find the constant of variation for the equation y = kx. In this example, we determine that y = 32 when x = 4, leading to a constant of variation of 8. Perfect for students in Grades 7-9.

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