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Variable Relationships Worksheet

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Variable Relationships Worksheet

Graph and table illustration

📊 Part 1: Understanding Variable Relationships

1. A mobile phone plan costs $15 per month plus $2 for each gigabyte of data used. Complete the table:

Rule: Cost = $15 + $2 × (number of gigabytes)

Gigabytes Used (x) Total Cost (y)
0 _______
2 _______
5 _______
10 _______
2. What happens to the total cost when the gigabytes used increases by 1?

It increases by $1

It increases by $2

It increases by $15

It stays the same

3. In this relationship, which is the independent variable?

Total cost

Gigabytes used

$15 monthly fee

$2 per gigabyte

📈 Part 2: Working with Rules and Patterns

4. For the rule y = 3x + 1, complete the table and describe the pattern:
x 1 2 3 4 5
y ____ ____ ____ ____ ____
5. Describe in words what happens to y when x increases by 1:
6. A car travels at a constant speed of 80 kilometres per hour. Which rule shows the relationship between time (t) in hours and distance (d) in kilometres?

d = 80 + t

d = 80t

d = t ÷ 80

t = 80d

7. Using your chosen rule from question 6, how far would the car travel in 3.5 hours?

🎯 Part 3: Real-Life Applications

8. Sarah is saving money for a new bike. She starts with $50 and saves $12 each week.

a) Write a rule to show the relationship between weeks (w) and total savings (s):

s = _______________

b) How much will Sarah have saved after 8 weeks? Show your working:

9. Look at this partially completed table showing temperature changes throughout the day:
Time (hours after midnight) 6 9 12 15
Temperature (°C) 8 14 20 26

Describe the relationship between time and temperature in this table:

10. Circle the statements that are TRUE about variable relationships:

The independent variable is the one we control or choose

In y = 5x, when x doubles, y also doubles

A table of values helps us see patterns in relationships

The dependent variable depends on the independent variable

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