1. **State the problem:** We need to find the total cost for 5 visits to the history museum for a member, given a linear relationship between the number of visits and total cost. 2. **Identify the formula:** The graph represents a linear function given by $$y = \frac{7}{6}x + 3$$ where $x$ is the number of visits and $y$ is the total cost. 3. **Calculate the total cost for 5 visits:** Substitute $x=5$ into the equation: $$y = \frac{7}{6} \times 5 + 3$$ 4. **Simplify the multiplication:** $$y = \frac{35}{6} + 3$$ 5. **Convert 3 to a fraction with denominator 6:** $$3 = \frac{18}{6}$$ 6. **Add the fractions:** $$y = \frac{35}{6} + \frac{18}{6} = \frac{53}{6}$$ 7. **Convert to decimal:** $$\frac{53}{6} \approx 8.83$$ 8. **Interpretation:** The total cost for 5 visits is approximately 8.83. 9. **Choose the closest answer:** Among the options $8.50$, $9$, $9.50$, and $7$, the closest is $9$. **Final answer:** The total cost for 5 visits is $9$.