📊 Part 1: Understanding Proportional Relationships

1. Sarah earns $15 per hour at her part-time job. Complete the table below:

Hours Worked	1	2	4	6
Total Pay ($)	____	____	____	____

2. Which of the following describes a linear proportional relationship?

A mobile phone plan with a $20 monthly fee plus $0.50 per text

Buying apples at $3 per kilogram

A taxi fare with a $5 flag fall plus $2 per kilometre

Petrol consumption at 8 litres per 100 kilometres

3. A recipe for anzac biscuits uses 2 cups of oats for every 1 cup of flour. If you use 6 cups of oats, how many cups of flour do you need?

4. The constant of proportionality in a linear relationship y = mx represents:

The y-intercept

The gradient (slope) of the line

The x-intercept

The point where the line crosses the y-axis

📈 Part 2: Tables, Graphs and Equations

5. A car travels at a constant speed of 80 kilometres per hour. Write the linear equation that represents the distance (d) travelled in time (t) hours:

d = __________

6. Look at this table showing the relationship between metres and centimetres:

Metres	1	2	3	5
Centimetres	100	200	300	500

a) What is the constant of proportionality? __________

b) Write the equation: c = __________

c) If this relationship was graphed, would the line pass through the origin (0,0)? __________

7. Circle the characteristics that ALL linear proportional relationships have:

The graph is a straight line

The line passes through the origin (0,0)

The equation has the form y = mx + b where b ≠ 0

The ratio between corresponding values is constant

The equation has the form y = mx

🧮 Part 3: Problem Solving

8. A New Zealand dollar is worth 0.62 US dollars. Complete this currency conversion problem:

a) Write an equation where u = US dollars and n = NZ dollars: u = __________

b) How many US dollars would you get for $50 NZ? __________

c) Explain why this is a proportional relationship:

9. Ben is filling a swimming pool with water. The pool fills at a rate of 250 litres per minute.

a) Create a table showing the volume of water after 2, 4, 6, and 10 minutes

b) Write the equation: V = __________

c) How long will it take to fill 2000 litres? __________ minutes

10. Explain in your own words what makes a relationship "linearly proportional" and give a real-life example:

Linear Proportion Foundations

Linear Proportion Foundations

📊 Part 1: Understanding Proportional Relationships

📈 Part 2: Tables, Graphs and Equations

🧮 Part 3: Problem Solving

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