1. **State the problem:** We are given the tuition costs for years 1, 4, and 5 at Northern Swim School and need to find the costs for years 2 and 3 assuming a constant rate of change. 2. **Identify known values:** - Year 1 cost: $168.50$ - Year 4 cost: $191.00$ - Year 5 cost: $198.50$ 3. **Understand the constant rate of change:** The tuition increases by the same amount each year. This means the cost forms an arithmetic sequence. 4. **Calculate the rate of change (slope):** The rate of change between year 1 and year 5 is $$\text{slope} = \frac{198.50 - 168.50}{5 - 1} = \frac{30}{4} = 7.5$$ 5. **Find the cost for years 2 and 3:** - Year 2 cost: $$168.50 + 7.5 = 176.00$$ - Year 3 cost: $$176.00 + 7.5 = 183.50$$ 6. **Verify with year 4 cost:** $$183.50 + 7.5 = 191.00$$ which matches the given data. 7. **Summary:** - Year 2 cost is $176.00$ - Year 3 cost is $183.50$ These points can be plotted on the graph at (2, 176) and (3, 183.5).