📊 Part 1: Identifying Proportional Relationships

1. Which of these represents a linear proportional relationship?

A taxi fare with a $3.50 base charge plus $2.20 per kilometre

Earning $18.50 per hour at a part-time job

A mobile phone plan with $25 monthly fee plus $0.50 per text

Buying concert tickets for $45 each plus $5 booking fee

2. In a proportional relationship, the graph will always:

Be a curved line

Pass through the origin (0,0)

Have a y-intercept of 5

Be a horizontal line

3. Look at this table showing the cost of apples:

Kilograms: 1, 2, 3, 4

Cost ($): 4.50, 9.00, 13.50, 18.00

The constant of proportionality is: __________

4. Check all the key features of linear proportional relationships:

Straight line graph

Passes through origin

Constant rate of change

Always has a y-intercept of 10

Can be written as y = mx

📝 Part 2: Working with Tables and Equations

5. Complete this table for a car travelling at a constant speed of 80 km/h:

Time (hours): 1, 2, 3, _____, 5

Distance (km): 80, _____, 240, 320, _____

6. Write the equation that represents the relationship in Question 5:

d = _______________ (where d = distance and t = time)

7. A recipe calls for 250g of flour for every 2 people served. Write the linear equation that shows the relationship between grams of flour (f) and number of people (p):

8. Sarah earns $16.50 per hour babysitting. How much will she earn for working 7 hours?

Show your working:

Answer: $ __________

🎯 Part 3: Real-World Applications

9. The exchange rate is $1 NZD = $0.65 USD. Complete this currency conversion table:

NZ Dollars: 10, 20, _____, 40, 50

US Dollars: 6.50, _____, 19.50, _____, 32.50

10. Explain in your own words what makes a relationship "proportional". Give one real-life example:

11. A gym charges $45 per month for membership. Is this a proportional relationship between months and total cost? Explain why or why not:

Linear Proportion Fundamentals

Linear Proportion Fundamentals

📊 Part 1: Identifying Proportional Relationships

📝 Part 2: Working with Tables and Equations

🎯 Part 3: Real-World Applications

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