1. The problem is to convert temperatures between Celsius (°C) and Fahrenheit (°F) and understand their relationship. 2. The formula to convert Celsius to Fahrenheit is: $$F = \frac{9}{5}C + 32$$ This means to find Fahrenheit, multiply Celsius by $\frac{9}{5}$ and then add 32. 3. Important points: - At $0^\circ C$, Fahrenheit is $32^\circ F$. - At $100^\circ C$, Fahrenheit is $212^\circ F$. 4. Let's verify these points using the formula: For $0^\circ C$: $$F = \frac{9}{5} \times 0 + 32 = 0 + 32 = 32$$ For $100^\circ C$: $$F = \frac{9}{5} \times 100 + 32 = 180 + 32 = 212$$ 5. This confirms the formula and the points on the graph. 6. The graph shows a linear relationship between Celsius and Fahrenheit with slope $\frac{9}{5}$ and y-intercept 32. Final answer: The conversion formula is $$F = \frac{9}{5}C + 32$$ which matches the graph and key temperature points.