If $y$ is inversely proportional to $x$, this means that:

$y = \frac{k}{x}$

where $k$ is the constant of proportionality.

Step 1: Find $k$ given $y = 4$ when $x = 9$

Using the given values: $4 = \frac{k}{9}$

Solving for $k$: $k = 4 \times 9 = 36$

So, the constant of proportionality $k = 36$.

Step 2: Write the variation equation in terms of $x$

Using $k = 36$, the equation becomes: $y = \frac{36}{x}$

Step 3: Find $y$ when $x = 17$

Substitute $x = 17$ into the equation: $y = \frac{36}{17}$

So, $y \approx 2.12$

Summary:

• Constant of proportionality $k = 36$
• Variation equation: $y = \frac{36}{x}$
• $y$ when $x = 17$: $y \approx 2.12$

Would you like further explanation or details?

Related Questions:

1. What happens to $y$ as $x$ approaches infinity in an inverse variation?
2. How does the graph of $y = \frac{36}{x}$ look compared to a linear function?
3. Can $y$ ever be zero in an inverse variation?
4. If $y$ is inversely proportional to $x^2$, how would the equation change?
5. How would the constant $k$ change if $y = 5$ when $x = 7$?

Tip:

In inverse variation, as one variable increases, the other decreases at a rate determined by $k$, showing the concept of proportional balancing.