In this worksheet, we will practice describing direct variation between two variables and using this to solve word problems.

**Q5: **

An object that weighs 120 N on the Earth weighs 20 N on the moon. Given that the weight of an object on Earth is directly proportional to its weight on the moon, find the weight of an object on the moon given that its weight on Earth is 126 N.

**Q6: **

Given that varies directly as , write an equation for in terms of using as a non-zero constant.

- A
- B
- C
- D

**Q8: **

Does vary directly with ? If so, what is the constant of variation?

2 | 4 | 6 | 8 | |

3 | 4 | 5 | 6 |

- A yes,
- B yes,
- C yes, 1
- Dno
- E yes,

**Q9: **

Determine whether the following statement is true or false: A directly proportional relationship can always be represented by a straight line graph passing through the origin.

- Atrue
- Bfalse

**Q11: **

Dalia uses cups of flour to make 20 biscuits. She makes a second batch using cups of flour to make 30 biscuits. Is the amount of flour she uses directly proportional to the number of biscuits she bakes?

- Ayes
- Bno

**Q12: **

Given that , and when , find the value of .

- A
- B
- C
- D

**Q13: **

Which of the following relations represents a direct variation between the two variables and ?

- A
- B
- C
- D

**Q14: **

Which of the given graphs represents the direct variation between and ?

- A(c)
- B(a)
- C(d)
- D(b)

**Q15: **

Given that varies directly with , and when , write an equation for in terms of .

- A
- B
- C
- D
- E

**Q16: **

A recipe for 4 people requires 440 g of spaghetti. The quantity of spaghetti is proportional to the number of people. What is the corresponding constant of proportionality (unit rate)?

**Q17: **

The total cost for pizzas is proportional to the number of pizzas, as shown in the graph.

Find the unit rate.

- A15Β’ per pizza
- B$30 per pizza
- C30Β’ per pizza
- D$15 per pizza
- E$60 per pizza

**Q18: **

The amount of meat required to feed a captive lion is given by the equation , where is the weight of the meat in kilograms needed to feed a lion for days. What is the unit rate of this proportional relationship?

**Q19: **

The amount of caffeine in a cup of coffee is roughly 95 mg. What is the constant of proportionality, or unit rate, between the amount of caffeine ingested and the number of cups taken?

**Q20: **

Points on a line are given in the table. Does vary directly with ? Is so, what is the constant of variation?

3 | 6 | 9 | 12 | |

2 | 4 | 6 | 8 |

- A no
- B yes,
- C yes,

**Q22: **

Engy decided to make pizzas. The graph shows the number of tomatoes needed for a given number of pizzas.

Determine which of the following statements is true.

- AThe point shows that she needs 5 tomatoes to make 10 pizzas.
- BThe point (6, 3) shows that to make 6 pizzas she needs 3 tomatoes.
- CThe point shows that she needs 5 tomatoes to make 10 pizzas.
- DThe point (3, 6) shows that to make 3 pizzas she needs 6 tomatoes.
- EThe point (8, 4) shows that she needs 8 tomatoes to make 4 pizzas.

**Q23: **

If , then .

- A
- B
- C
- D

**Q25: **

The instructions on a packet of fertiliser state that 500 g will treat an area of 60 square metres if mixed correctly. How much fertiliser is needed to treat a garden whose area is 100 square metres? Give your answer to the nearest gram if necessary.

- A 600 g
- B 300 g
- C 450 g
- D 833 g
- E 124 g