1. **Problem Statement:** We have two taxi services with costs represented by parallel lines on a graph. The Speedy Taxi Service charges a base cost of $1.80 plus $0.10 per kilometre. The Economic Taxi Service has a lower base cost and a smaller rate per kilometre. 2. **Given:** - Speedy Taxi Service cost equation: $$c = 1.80 + 0.10k$$ - Economic Taxi Service line is parallel to Speedy Taxi Service, so it has the same slope (rate per km) but a different base cost. - From the graph, Economic Taxi Service base cost is approximately $1.40. 3. **(a) Write the equation for Economic Taxi Service:** Since the lines are parallel, the slope is the same: $0.10$ per km. Base cost for Economic Taxi Service is $1.40$. Therefore, the cost equation is: $$c = 1.40 + 0.10k$$ 4. **(b)(i) Calculate cost for 7 km using Economic Taxi Service:** Substitute $k=7$ into the equation: $$c = 1.40 + 0.10 \times 7 = 1.40 + 0.70 = 2.10$$ Bruce will pay $2.10$ for 7 km. 5. **(b)(ii) Calculate distance for $2.40 cost:** Set $c=2.40$ and solve for $k$: $$2.40 = 1.40 + 0.10k$$ Subtract 1.40 from both sides: $$2.40 - 1.40 = 0.10k$$ $$1.00 = 0.10k$$ Divide both sides by 0.10: $$k = \frac{1.00}{0.10} = 10$$ Bruce can travel 10 km for $2.40 using the Economic Taxi Service. **Final answers:** (a) $$c = 1.40 + 0.10k$$ (b)(i) $2.10$ (b)(ii) $10$ km