Direct variation is a relationship between two variables. In this case, y is directly proportional to x. We say y varies directly with x if:
[tex]\begin{gathered} y=kx \\ \text{ Where k is a constant} \end{gathered}[/tex]
On the other hand, inverse variation is another relationship between two variables. In this case, y is inversely proportional to x. We say y varies inversely with x if:
[tex]y=\frac{k}{x}[/tex]
Now, if we combine the two previous definitions, we have:
[tex]\begin{gathered} y=kx\Rightarrow\text{ Because y varies directly with x} \\ y=\frac{kx}{z}\Rightarrow\text{ Because y varies inversely with z} \end{gathered}[/tex]
Therefore, y varies directly as x and inversely as z can be modeled by the equation
[tex]$\boldsymbol{y=\frac{kx}{z}}$[/tex]
