1. **Problem statement:** Esther paints 7 faces every 21 minutes, spending the same amount of time on each face. We want to write an equation relating $f$, the number of faces painted, and $m$, the time spent painting in minutes. 2. **Understanding the problem:** Since Esther paints 7 faces in 21 minutes, the rate of painting is $\frac{7}{21}$ faces per minute. 3. **Simplify the rate:** $$\frac{7}{21} = \frac{1}{3}$$ So, Esther paints $\frac{1}{3}$ of a face per minute. 4. **Form the equation:** If $f$ is the number of faces painted and $m$ is the time in minutes, then $$f = \frac{1}{3} m$$ This means the number of faces painted is one third of the minutes spent painting. 5. **Interpretation:** For every 3 minutes, Esther paints 1 face. This linear relationship allows us to find $f$ for any given $m$. **Final equation:** $$f = \frac{1}{3} m$$