📱 Part 1: Real-Life Linear Equations

1. A mobile phone plan costs $25 per month plus $0.50 for each text message sent. Write a linear equation to represent the total monthly cost (C) based on the number of text messages (t).

2. Sarah is cycling at a constant speed of 15 kilometres per hour. She started her journey 5 kilometres from home. Write an equation for her distance (d) from the starting point after t hours.

3. A cinema charges $12 per ticket plus a $3 booking fee per transaction. If the total cost is $51, how many tickets were purchased?

📊 Part 2: Creating Data Tables

4. Using the phone plan equation from Question 1 (C = 25 + 0.5t), complete this table:

Number of texts (t): 0, 10, 20, 30, 40

Total cost (C): _____, _____, _____, _____, _____

5. For the cycling equation from Question 2, calculate Sarah's distance after:

After 1 hour: _______ km

After 2 hours: _______ km

After 3 hours: _______ km

📈 Part 3: Graphing Linear Equations

6. Plot the phone plan data from Question 4 on the coordinate plane below. Label your axes clearly with units.

7. What does the gradient (slope) of your phone plan graph represent in real life?

8. What does the y-intercept of your phone plan graph represent?

🎯 Part 4: Interpreting Graphs

9. Circle the correct answer: In the equation y = 3x + 7, what is the gradient?

3

7

x

y

10. Check all statements that are true about linear graphs:

They form straight lines

They can curve

They have a constant rate of change

They always pass through the origin

🧮 Part 5: Problem Solving

11. A taxi company charges $3.50 for the first kilometre and $2.20 for each additional kilometre. Write an equation for the total cost (C) for a journey of d kilometres (where d ≥ 1).

12. Using your taxi equation, calculate the cost of a 8-kilometre journey.

13. If a taxi journey costs $25.90, how many kilometres was the trip? Show your working.

🔗 Part 6: Matching Activity

14. Match each equation with its correct description:

1. y = 5x + 10

2. y = 2x

3. y = -3x + 15

4. y = 8

A. Horizontal line

B. Line through origin with positive slope

C. Line with negative slope

D. Line with y-intercept of 10

💭 Part 7: Reflection

15. Explain in your own words what a linear equation represents in real life. Give an example.

16. Why is it useful to represent linear equations as graphs? What information can you get from a graph that might be harder to see from just the equation?