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Linear Proportion Fundamentals

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Linear Proportion Fundamentals

For each question, show working where appropriate. Give units with numerical answers.

Recognising Proportional Relationships

1.Which situation is represented by a proportional relationship?

A shuttle charges a $6 launch fee, then $3 per passenger.
A satellite sends 24 data packets every second at a steady rate.
A mission costs $12,000 to begin, plus $800 per day.
A technician earns $28 per hour plus a $50 bonus.

2.A straight-line graph represents a proportional relationship. Which feature must it have?

It crosses the vertical axis at 4.
It passes through (0, 0).
It has a constant value of y.
It curves upwards from the origin.

3.A spacecraft travels 135 km in 3 minutes at a constant rate. Find the constant of proportionality in kilometres per minute.

4.Select every statement that is true of a linear proportional relationship.

Its graph is a straight line.
Its graph passes through the origin.
The ratio y/x is constant for non-zero x.
Its equation can be written y = mx.
Its y-intercept is always 1.

Tables and Equations

5.A probe travels at a constant speed of 72 km/h. Complete the missing values in the table.

Time (h): 1, 2, 3, 4, 5

Distance (km): 72, ____, 216, ____, ____

6.Using d for distance in kilometres and t for time in hours, write an equation for a probe travelling at 72 km/h.

7.A life-support unit uses 840 litres of oxygen over 7 days at a constant rate. Write an equation linking oxygen used, O litres, and time, t days.

8.Ana earns $24.80 per hour for mission-support work. How much does she earn for 6.5 hours?

9.A training mix uses 180 g of powder for every 3 litres of water. Write an equation for the powder mass, m grams, needed for w litres of water.

Applying Proportional Reasoning

10.The exchange rate is NZ$1 = US$0.62. Complete the conversions.

NZ dollars: 10, 25, 40, 55

US dollars: ____, ____, ____, ____

11.Explain how to decide whether a relationship is proportional, and give one example of a proportional relationship.

12.A space station charges a fixed NZ$18 docking fee for each delivery, regardless of how many kilograms of cargo are delivered. Is the total fee proportional to cargo mass? Explain using the proportionality test.