📊 Part 1: Completing Tables and Identifying Linear Relationships

1. Complete the table of values for y = 3x + 2:

x: -2, -1, 0, 1, 2

y: _____, _____, _____, _____, _____

2. Calculate the first differences for the y-values above:

First differences: _____, _____, _____, _____

3. Is this relationship linear? Explain why:

4. Complete the table for y = -2x + 5:

x: 0, 1, 2, 3, 4

y: _____, _____, _____, _____, _____

5. Complete the table for y = 0.5x - 1:

x: -2, 0, 2, 4, 6

y: _____, _____, _____, _____, _____

6. Which of these tables shows a linear relationship?

Table A: x = 1,2,3,4 and y = 2,4,8,16

Table B: x = 1,2,3,4 and y = 5,7,9,11

Table C: x = 1,2,3,4 and y = 1,4,9,16

7. Complete this table and determine if it's linear:

x: -1, 0, 1, 2, 3

y = 4x - 3: _____, _____, _____, _____, _____

First differences: _____, _____, _____, _____

Is it linear? _____

📈 Part 2: Plotting and Finding Rules

8. Plot the points from question 1 on the grid below. Use a ruler to draw the line.

9. From the graph you've plotted, identify:

a) The y-intercept: _____

b) The gradient (slope): _____

10. Plot these points and draw the line: (-1, 4), (0, 2), (1, 0), (2, -2)

What is the rule for this line? y = _________

11. A linear relationship passes through points (0, 4) and (2, 10). Find the rule:

Rule: y = _________

12. Find the rule for a line passing through (1, 7) and (3, 13):

Rule: y = _________

13. Match each table to its correct linear rule:

Table: (0,1), (1,3), (2,5)

Table: (0,0), (1,4), (2,8)

Table: (0,6), (1,4), (2,2)

Table: (0,-2), (1,1), (2,4)

y = 4x

y = 2x + 1

y = -2x + 6

y = 3x - 2

🌍 Part 3: Real-World Applications

14. A mobile phone plan costs $25 per month plus $0.50 per GB of data used.

a) Write a rule for the total cost (C) in terms of GB used (g): C = _________

b) What would be the cost for using 12 GB? $______

c) If someone's bill was $40, how many GB did they use? _____ GB

15. A taxi charges $3.50 for the first kilometer and $1.20 for each additional kilometer.

a) Write a rule for the total cost (C) for traveling d kilometers: C = _________

b) How much would a 8-kilometer trip cost? $______

c) If a trip cost $15.70, how many kilometers was it? _____ km

16. A water tank contains 500 liters and drains at 15 liters per minute.

a) Write a rule for water remaining (W) after t minutes: W = _________

b) How much water remains after 20 minutes? _____ liters

c) When will the tank be empty? _____ minutes

17. A gym membership costs $80 to join plus $25 per month.

a) Write a rule for total cost (T) after m months: T = _________

b) What's the total cost after 6 months? $______

c) Complete this table:

Months: 0, 3, 6, 9, 12

Total Cost: $_____, $_____, $_____, $_____, $_____

🚀 Part 4: Challenge Problems and Extensions

18. Without plotting, determine which line is steeper:

y = 5x + 2

y = -7x + 1

y = 3x - 4

19. Challenge: Find the rule for a line with gradient -3 that passes through point (2, 8):

Rule: y = _________

20. Advanced: Two lines intersect at point (4, 11). One line has rule y = 2x + 3. If the other line passes through (0, 7), what is its rule?

Rule: y = _________

21. Extension: A linear function has these properties: when x increases by 2, y decreases by 6, and it passes through (1, 10). Find the rule:

Rule: y = _________

22. Problem Solving: The temperature in degrees Celsius (C) and Fahrenheit (F) are related by a linear relationship. Water freezes at 0°C (32°F) and boils at 100°C (212°F).

a) Find the rule connecting F and C: F = _________

b) What is 25°C in Fahrenheit? _____°F

c) What temperature in Celsius equals 68°F? _____°C

23. Reflection: Explain in your own words how you can tell if a relationship is linear just by looking at a table of values:

24. Creative Challenge: Create your own real-world linear relationship problem. Write the scenario, the rule, and ask two questions about it:

Linear Relationships Plotting Worksheet

Linear Relationships Plotting Worksheet

📊 Part 1: Completing Tables and Identifying Linear Relationships

📈 Part 2: Plotting and Finding Rules

🌍 Part 3: Real-World Applications

🚀 Part 4: Challenge Problems and Extensions

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