1. **State the problem:** We are given a table of distances and fares and need to construct a linear function that models the fare based on distance. 2. **Find the slope $m$:** The slope formula is $m = \frac{\text{change in fare}}{\text{change in distance}}$. Using points $(0,3)$ and $(4,5)$: $$m = \frac{5 - 3}{4 - 0} = \frac{2}{4} = \frac{\cancel{2}}{\cancel{4}} = \frac{1}{2}$$ 3. **Find the starting fare $b$:** This is the fare when distance $d=0$ km, which from the table is $b=3$. 4. **Write the linear equation:** Using the slope-intercept form $\text{Fare} = md + b$: $$\text{Fare} = \frac{1}{2}d + 3$$ 5. **Complete the table using the equation:** - For $d=0$: $\text{Fare} = \frac{1}{2} \times 0 + 3 = 3$ - For $d=2$: $\text{Fare} = \frac{1}{2} \times 2 + 3 = 1 + 3 = 4$ - For $d=4$: $\text{Fare} = \frac{1}{2} \times 4 + 3 = 2 + 3 = 5$ - For $d=6$: $\text{Fare} = \frac{1}{2} \times 6 + 3 = 3 + 3 = 6$ - For $d=8$: $\text{Fare} = \frac{1}{2} \times 8 + 3 = 4 + 3 = 7$ - For $d=10$: $\text{Fare} = \frac{1}{2} \times 10 + 3 = 5 + 3 = 8$ Thus, the completed table is: | d (km) | Fare (AED) | |--------|------------| | 0 | 3 | | 2 | 4 | | 4 | 5 | | 6 | 6 | | 8 | 7 | | 10 | 8 |