Linear Equations and Inequalities

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📊 Part 1: Linear Relationships

1. A taxi company in Auckland charges a base fare of $3.50 plus $2.40 per kilometre. Which equation represents the total cost (C) for a journey of d kilometres?

C = 2.40d + 3.50

C = 3.50d + 2.40

C = 2.40 + 3.50

C = 2.40d

2. Look at this table showing the cost of hiring a hall in Wellington:

Hours: 1, 2, 3, 4

Cost ($): 85, 120, 155, 190

What is the hourly rate? $_______ per hour

What is the fixed cost? $_______

3. Which of the following are linear relationships? (Select all that apply)

y = 3x + 7

y = x²

2x + 3y = 12

y = 5

⚖️ Part 2: Solving Equations and Inequalities

4. Solve for x: 3x + 8 = 23

Answer: x = _______

5. A student needs at least 75 marks to pass a test. If the test has 15 questions worth 2 marks each, plus a bonus section worth b marks, write an inequality to represent this situation.

6. Solve the inequality: 2x - 5 ≥ 11

Answer: x _____ _______