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Variable Relationships Worksheet
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Variable Relationships Worksheet
Use each rule or table to explore how one variable changes when another changes. Show calculations where asked.
Reading relationships
1.A bike hire shop charges a $7 booking fee plus $4 for each hour hired. The rule is c = 7 + 4h, where h is hours and c is the cost in dollars. Find the cost for 0, 2, 4 and 6 hours.
Hours, h
0
2
4
6
Cost, c ($)
2.In the bike hire rule c = 7 + 4h, what happens to the cost when the hire time increases by one hour?
- It increases by $1.
- It increases by $4.
- It increases by $7.
- It stays the same.
3.For the bike hire rule c = 7 + 4h, which variable is independent?
- The cost, c
- The hire time, h
- The booking fee, 7
- The hourly charge, 4
Rules and patterns
4.Use the rule y = 5x − 2. Find y when x = 1, 2, 3, 4 and 5.
x
1
2
3
4
5
y
5.For y = 5x − 2, describe how y changes whenever x increases by 1.
6.A ferry travels at a constant speed of 24 kilometres per hour. Which rule gives its distance d in kilometres after t hours?
- d = 24 + t
- d = 24t
- d = t ÷ 24
- t = 24d
7.Using d = 24t for the ferry journey, calculate the distance travelled in 2.5 hours.
Variable relationships in everyday situations
8.Ivy has $35 saved and puts aside another $9 each week. Write a rule for her savings s after w weeks, then calculate her savings after 7 weeks.
Time after midnight (hours)
7
10
13
16
Temperature (°C)
9
15
21
27
9.Using the temperature table above, explain how the temperature changes as time increases.
10.Select every true statement about variable relationships.
- The independent variable is often the input we choose or control.
- For y = 6x, doubling x also doubles y.
- A table can help show how two variables are related.
- The dependent variable changes in response to the independent variable.
3 printable pages
Page 1
Page 2
Page 3
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