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The problem asks to write a direct variation equation relating \(x\) and \(y\) based on the given information \(y = 9\) when \(x = 8\), and then to find the value of \(y\) when \(x = 16\).

### Step 1: Writing the direct variation equation
In direct variation, the relationship between \(x\) and \(y\) is given by the formula:
\[
y = kx
\]
where \(k\) is the constant of variation.

To find \(k\), use the values given: \(y = 9\) when \(x = 8\). Substitute these into the equation:
\[
9 = k \cdot 8
\]
Solve for \(k\):
\[
k = \frac{9}{8}
\]

Thus, the direct variation equation is:
\[
y = \frac{9}{8}x
\]

### Step 2: Finding \(y\) when \(x = 16\)
Now, substitute \(x = 16\) into the equation to find \(y\):
\[
y = \frac{9}{8} \times 16 = 18
\]

So, when \(x = 16\), \(y = 18\).

Would you like more details on any of these steps?

Here are some related questions for further practice:
1. What is the value of \(k\) if \(y = 12\) when \(x = 6\)?
2. If \(y = 5x\), what is the value of \(y\) when \(x = 20\)?
3. How does the direct variation equation change if \(y = -10\) when \(x = 2\)?
4. If \(y\) varies directly with \(x\) and \(y = 15\) when \(x = 5\), find \(y\) when \(x = 10\).
5. What happens to \(y\) if \(x\) is doubled in a direct variation equation?

**Tip:** In a direct variation, \(y\) is always proportional to \(x\), so as \(x\) increases or decreases, \(y\) does the same in direct proportion.

Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x = 16. y = 9 when x = 8.

Learn how to write a direct variation equation that relates x and y, based on y = 9 when x = 8. The solution includes finding the value of y when x = 16. Suitable for students in Grades 7-9.

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