1. **State the problem:** We are given data for distance traveled (in km) and corresponding fare (in AED) and need to construct a linear function that models this relationship. 2. **Formula used:** The linear function is generally written as $$\text{Fare} = md + b$$ where $m$ is the slope (rate of change of fare per km) and $b$ is the starting fare (fare at 0 km). 3. **Find the slope $m$:** Using two points from the data, for example $(0,3)$ and $(4,5)$, $$m = \frac{\text{change in fare}}{\text{change in distance}} = \frac{5 - 3}{4 - 0} = \frac{2}{4} = 0.5$$ 4. **Find the starting fare $b$:** From the data, when distance $d=0$, fare is 3, so $b=3$. 5. **Write the equation:** Substitute $m=0.5$ and $b=3$ into the formula: $$\text{Fare} = 0.5d + 3$$ 6. **Complete the table:** Calculate fare for given distances using the equation: - For $d=0$: $\text{Fare} = 0.5 \times 0 + 3 = 3$ - For $d=2$: $\text{Fare} = 0.5 \times 2 + 3 = 4$ - For $d=4$: $\text{Fare} = 0.5 \times 4 + 3 = 5$ - For $d=6$: $\text{Fare} = 0.5 \times 6 + 3 = 6$ - For $d=8$: $\text{Fare} = 0.5 \times 8 + 3 = 7$ - For $d=10$: $\text{Fare} = 0.5 \times 10 + 3 = 8$ This confirms the linear function correctly models the fare based on distance. **Final answer:** The linear function is $$\boxed{\text{Fare} = 0.5d + 3}$$