1. **State the problem:** We want to understand the relationship between the number of batteries $x$ and the total cost $y$ based on the given data and equation. 2. **Identify the formula:** The equation given is $$y = 3.5x + 28$$ which represents a linear function where $y$ is the total cost and $x$ is the number of batteries. 3. **Explain the components:** In this equation, $3.5$ is the cost per battery, and $28$ is the fixed cost (likely the charger or base cost). 4. **Check the data against the equation:** For example, when $x=1$, $$y = 3.5(1) + 28 = 3.5 + 28 = 31.5$$ which does not match the table value $39.10$. This suggests the equation might be an approximation or from a different source. 5. **Interpret the graph and table:** The table shows increasing costs by $2.10$ per additional battery, which differs from the $3.5$ per battery in the equation. 6. **Conclusion:** The equation $y = 3.5x + 28$ models a linear cost with a fixed base and a per-battery cost of $3.5$. The table and graph suggest a different rate, so the equation may represent a different pricing model. **Final answer:** The cost function is $$y = 3.5x + 28$$ where $x$ is the number of batteries and $y$ is the total cost.