Questions: y varies inversely with x. y is 2 when x is 9. What is y when x is 6?

Solution Steps

To solve this problem, we need to use the concept of inverse variation. When two variables vary inversely, their product is constant. Given that $y$ is 2 when $x$ is 9, we can find the constant of variation. Then, we use this constant to find $y$ when $x$ is 6.

Given that $y$ varies inversely with $x$, we know that $y \cdot x = k$, where $k$ is a constant. We are given $y = 2$ when $x = 9$. Therefore, we can find $k$ as follows: $$k = y \cdot x = 2 \cdot 9 = 18$$

We need to find $y$ when $x = 6$. Using the constant of variation $k = 18$, we can set up the equation: $$y \cdot 6 = 18$$ Solving for $y$: $$y = \frac{18}{6} = 3$$

Final Answer