So, you have
[tex]\frac{\text{ \$45}}{9\text{ mugs}}\Rightarrow\text{ Rate}[/tex]On the other hand
[tex]\begin{gathered} \frac{\text{ \$45}}{9\text{ mugs}} \\ \text{ Divide by 9 in the numerator and denominator} \\ \frac{\text{ }\frac{\text{\$45}}{9}}{\frac{9\text{ mugs}}{9}}=\frac{\text{ \$}5}{1\text{ mug}}\Rightarrow\text{ Price per mug} \\ \text{ Then} \\ \frac{\text{ \$}5}{1\text{ mug}}\Rightarrow\text{ Unit rate} \end{gathered}[/tex]Therefore, the rate is
[tex]\frac{\text{ \$45}}{9\text{ mugs}}[/tex]and the unit rate is
[tex]\frac{\text{ \$}5}{1\text{ mug}}[/tex]