1. **State the problem:** We need to find the equation that represents the proportional relationship between the number of pencils $p$ and the cost $c$ given the data points: $(9, 2.34)$, $(12, 3.12)$, and $(16, 4.16)$. 2. **Formula for proportional relationships:** If two quantities are proportional, then $c = kp$ where $k$ is the constant of proportionality. 3. **Find the constant of proportionality $k$:** Use one data point, for example $(9, 2.34)$: $$k = \frac{c}{p} = \frac{2.34}{9} = 0.26$$ 4. **Check with other points:** For $(12, 3.12)$: $$\frac{3.12}{12} = 0.26$$ For $(16, 4.16)$: $$\frac{4.16}{16} = 0.26$$ All give the same $k=0.26$, confirming the proportionality. 5. **Write the equation:** $$c = 0.26p$$ 6. **Interpretation:** The cost $c$ is $0.26$ times the number of pencils $p$, so option A is correct. **Final answer:** $c = 0.26p$