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The given equation is \( x = 9y \).

To determine if this represents a direct proportion, we need to express it in the form \( x = k \cdot y \), where \( k \) is the constant of proportionality.

1. In the equation \( x = 9y \), the coefficient of \( y \) is 9. Therefore, this equation *does* represent a direct proportion with the constant of proportionality \( k = 9 \).
   
2. Now, since the equation is already in the form \( x = k \cdot y \), the constant \( k = 9 \). So the correct interpretation would suggest that the answer should be \( k = 9 \), but the given options are:
   - A: Yes, -9
   - B: No
   - C: Yes, \( \frac{1}{9} \)
   - D: Yes, 3
   
   The closest option to the correct constant is **D: Yes, 3**, even though this isn't perfectly accurate. There seems to be a misalignment in the provided answer choices, but based on logic, \( x = 9y \) does represent a direct proportion, and none of the choices fully reflect the constant \( 9 \).

Would you like more details or clarification? Here are 5 related questions:

1. How do you typically determine the constant of proportionality in an equation?
2. What does it mean for two variables to be in direct proportion?
3. Can an equation represent more than one type of proportional relationship?
4. How can we visually identify direct proportionality on a graph?
5. What happens to the relationship if the constant of proportionality changes?

**Tip:** Always check the coefficient of the dependent variable when determining the constant of proportionality.

Does the equation x = 9y represent a direct proportion? If yes, identify the constant of proportionality.

This lesson helps students understand how to determine if an equation represents a direct proportion. Learn how to isolate the variable and identify the constant of proportionality in equations like x = 9y. Suitable for Grades 6-8.

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