Step 1 :First, we need to find the equations where \(k\) is equal to a constant divided by \(m\). In other words, we are looking for equations in the form of \(k = \frac{C}{m}\), where \(C\) is a constant.
Step 2 :Given equations are: \(k=\frac{m}{2}\), \(k=2m\), \(k=m-2\), \(k=m+2\), and \(k=\frac{2}{m}\).
Step 3 :Among these equations, only \(k=\frac{2}{m}\) is in the form of \(k = \frac{C}{m}\), where \(C = 2\).
Step 4 :\(\boxed{k = \frac{2}{m}}\) is the only equation in which \(k\) is inversely proportional to \(m\).