1. **State the problem:** Write an equation that represents the proportional relationship between the price $P$ of canned corn and the number of cans $c$ purchased. 2. **Analyze the graph:** The graph shows a straight line passing through points $(0,1)$, $(3,3)$, and $(5,5)$. 3. **Check if the relationship is proportional:** A proportional relationship must pass through the origin $(0,0)$, but here the line passes through $(0,1)$, so it is not proportional. 4. **Write the linear equation:** The line has a y-intercept at 1, so the equation is of the form $$P = mc + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. **Calculate the slope $m$:** Using points $(3,3)$ and $(0,1)$, $$m = \frac{3 - 1}{3 - 0} = \frac{2}{3}$$ 6. **Write the equation:** $$P = \frac{2}{3}c + 1$$ 7. **Interpretation:** The price increases by $\frac{2}{3}$ for each additional can, starting at a base price of 1 when no cans are purchased. **Final answer:** $$P = \frac{2}{3}c + 1$$