Applied Algebra Adventure

Name:

Date:

Linear equations and graphs illustration

📊 Part 1: Linear Relationships in Real Life

1. A taxi company charges $5 for the initial fare plus $2.50 for every kilometre travelled. Which equation represents the total cost (C) for travelling x kilometres?

C = 5x + 2.50

C = 2.50x + 5

C = 7.50x

C = 5 + 2.50

2. In the equation y = 3x - 4, what does the number 3 represent?

The y-intercept

The gradient (slope)

The x-intercept

A constant term

3. A mobile phone plan costs $25 per month plus $0.30 for each text message sent. Complete the table below:

Number of texts (x): 0, 10, 20, 50

Total cost ($): _____, _____, _____, _____

4. Write the equation for the mobile phone plan in Question 3:

Total cost = _____________

🎯 Part 2: Problem Solving

5. A school fundraiser sells cupcakes for $3 each, plus a $40 stall rental fee. If they need to raise at least $160, how many cupcakes must they sell? Show your working:

6. The equation y = -2x + 8 represents the temperature (y°C) at different altitudes (x km above sea level). What is the temperature at sea level (0 km altitude)?

7. A photographer charges $120 for a photo session plus $18 for each printed photo. If a customer's total bill was $210, how many printed photos did they order? Show your equation and solution:

🚀 Part 3: Create Your Own

8. Think of a real-world situation that involves a linear relationship (like gym membership, pizza delivery, etc.). Describe your scenario and write the equation:

Scenario:

Equation: _______________

9. Using your equation from Question 8, create three points (x, y) that would appear on the graph:

Point 1: (_____, _____)

Point 2: (_____, _____)

Point 3: (_____, _____)