📚 Part 1: Understanding Linear Models

1. A taxi company charges $5.50 per kilometre plus a $12.00 booking fee. Which equation represents the total cost (C) for travelling d kilometres?

C = 5.50d + 12.00

C = 12.00d + 5.50

C = 5.50 + 12.00 + d

C = (5.50 + 12.00) × d

2. In the linear equation y = mx + c, what do the letters m and c represent?

m represents the _________________ and c represents the _________________

3. Which of these situations could be modelled using a linear equation? (Check all that apply)

Monthly mobile phone plan with fixed cost plus data charges

Population growth of bacteria doubling every hour

Cost of hiring a car per day

Temperature change at a constant rate

4. A paddle boat hire costs $30 per hour plus a $10 registration fee. Complete the table by substituting values into the equation C = 30h + 10:

Hours (h)	Cost (C)
1	$_______
3	$_______
5	$_______

📊 Part 2: Creating and Interpreting Linear Models

5. A water tank contains 500 litres and drains at a rate of 25 litres per hour. Write a linear equation to represent the amount of water (W) remaining after t hours.

W = _________________

6. Using your equation from Question 5, how much water will be left after 8 hours?

7. A student's phone plan costs $45 per month plus $0.80 for each gigabyte of data used. If the monthly bill was $61.40, how many gigabytes of data were used?

8. Look at this linear graph showing temperature change over time. The temperature starts at 15°C and increases by 3°C every hour.

a) Write the equation: T = _________________

b) What will the temperature be after 4 hours? _________°C

c) After how many hours will the temperature reach 30°C? _________ hours

🎯 Part 3: Real-World Applications

9. A plumber charges a $80 call-out fee plus $65 per hour for labour. Create a linear model and explain what each part represents in the context.

10. Extension Challenge: Two mobile phone companies offer different plans:
• Company A: $40 per month + $0.50 per GB
• Company B: $25 per month + $1.20 per GB
Write equations for both companies and determine when both plans cost the same amount.