Question

Does the equation model direct variation, inverse variation, or neither? \(x=\frac{7}{y}\)

Short answer

The given equation represents an inverse variation.

Step-by-step solution

Identify the given equation

The provided equation is \(x=\frac{7}{y}\)

Compare with standard forms of direct and inverse variation

The standard form of direct variation is \(y=kx\) and that of inverse variation is \(y=\frac{k}{x}\) or \(x=\frac{k}{y}\). Comparing the given equation with these forms, it is clear that it matches the form of inverse variation \(x=\frac{k}{y}\), with the constant of variation being 7.

Conclusion

Given the comparison in step 2, the equation \(x=\frac{7}{y}\) is an inverse variation equation.