https://file.aiquickdraw.com/mathbot/file/1726014361674lgw4y7v6.jpg

The problem in the image says:

"If \( x \) and \( y \) vary directly and \( y = 5 \) when \( x = 15 \), find \( y \) when \( x = 3 \)."

### Solution:
Since \( x \) and \( y \) vary directly, we can express this relationship as:

\[
y = kx
\]

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

1. First, find \( k \) using the given values \( y = 5 \) and \( x = 15 \):

\[
5 = k \times 15
\]

\[
k = \frac{5}{15} = \frac{1}{3}
\]

2. Now that we know \( k = \frac{1}{3} \), use this to find \( y \) when \( x = 3 \):

\[
y = \frac{1}{3} \times 3 = 1
\]

Thus, when \( x = 3 \), \( y = 1 \).

Would you like more details or have any questions about this solution?

Here are 5 related questions to explore:
1. What is the formula for direct variation?
2. How do you calculate the constant of proportionality in direct variation?
3. Can you apply the same method for inverse variation problems?
4. What happens to \( y \) if \( x \) doubles in a direct variation relationship?
5. How would the solution change if \( x \) and \( y \) varied inversely instead?

**Tip:** In any direct variation problem, knowing one pair of corresponding \( x \) and \( y \) values helps you find the constant and solve for other pairs.

If x and y vary directly and y is 5 when x is 15, find y when x is 3.

Solve a direct variation problem where y is 5 when x is 15, and find y when x is 3. Learn how to apply the direct variation formula y = kx and calculate the constant of proportionality. Suitable for students in Grades 6-8.

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