For each equation, determine whether it represents a direct variation, an inverse variation, or neither. Find the constant of variation when one exists and write it in simplest form. \( \begin{array}{l}\frac{10}{y}=x \\ \text { Direct variation } \\ \text { Constant of variation: } \quad k=\square \\ \text { Inverse variation } \\ \begin{array}{l}\text { Neither } \\ \text { Constant of variation: }\end{array} \\ \begin{array}{l}\text { Direct variation } \\ \text { Constant of variation: }\end{array} \\ \text { Inverse variation } \\ \text { Constant of variation: }\end{array} \)

To determine the type of variation for the equation \(\frac{10}{y} = x\), we can rearrange it to the form \(y = \frac{10}{x}\). This shows that as \(x\) increases, \(y\) decreases, indicating an inverse variation. The constant of variation (k) can be found as follows: \(k = 10\). For the second part, the equation represents neither a direct nor inverse variation if it does not fit the established forms of \(y = kx\) (direct) or \(y = \frac{k}{x}\) (inverse). Additional examples of such equations include \(y = x^2 + 1\) or \(y = \sin(x)\), which do not exhibit a consistent relationship of proportionality that defines direct or inverse variations.