Linear Equations and Graphs

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📈 Part 1: Understanding Linear Equations

1. For the equation y = 3x + 2, what is the gradient and y-intercept?

Gradient = 2, y-intercept = 3

Gradient = 3, y-intercept = 2

Gradient = 5, y-intercept = 0

Gradient = 1, y-intercept = 5

2. Which equation represents a line with a negative gradient?

y = 2x + 5

y = -3x + 1

y = x + 4

y = 0.5x - 2

3. Write the linear equation for this table of values:

x: 0, 1, 2, 3

y: 5, 7, 9, 11

Equation: y = ___________

4. A taxi fare starts at $4 and costs $2 per kilometre. Which equation represents the total cost (C) for travelling d kilometres?

C = 4d + 2

C = 2d + 4

C = 6d

C = d + 6

📊 Part 2: Graphing and Problem Solving

5. Plot the equation y = -x + 4 on the grid below. Mark at least 3 points clearly.

6. A phone plan charges $10 per month plus $0.20 per text message. Write an equation to represent the total cost (C) in dollars based on the number of text messages (t).

7. Show your working to find the gradient between the points (1, 3) and (4, 9).

8. From the graph of a straight line, you read two points: (0, -2) and (3, 4). Write the equation of this line in the form y = mx + c.

🎯 Part 3: Real-World Applications

9. A water tank starts with 50 litres and drains at a rate of 5 litres per minute. Write an equation for the amount of water (W) remaining after t minutes, then sketch the graph.

Equation: W = ___________

10. Explain in your own words what the gradient tells us about a linear relationship. Give an example from real life.