Which type of relationship is shown in the graph? Give a reason for the answer

Here are the solutions to Question 2:

2.1.1
The type of relationship shown in the graph is an inverse proportion (or inverse relationship).
Reason: As the number of hours per week increases, the number of weeks required to complete the flying time decreases. This means that the product of the two variables is constant (24 hours).

2.1.2
The total flying time is 24 hours. The relationship is:

$$\text{No. of hours per week} \times \text{No. of weeks} = 24$$

Therefore, $\text{No. of weeks} = \frac{24}{\text{No. of hours per week}}$.

• A: When No. of weeks = 12: $$12 = \frac{24}{A}$$ $$A = \frac{24}{12} = 2$$ So, A = $\boxed{2}$
• C: When No. of hours = 4: $$C = \frac{24}{4} = 6$$ So, C = $\boxed{6}$
• B: When No. of weeks = 3: $$3 = \frac{24}{B}$$ $$B = \frac{24}{3} = 8$$ So, B = $\boxed{8}$
• D: When No. of hours = 24: $$D = \frac{24}{24} = 1$$ So, D = $\boxed{1}$

2.1.3

• Independent variable: Number of hours per week
• Dependent variable: Number of weeks