# Lesson Worksheet: Direct Variation Mathematics • 7th Grade

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

**Q7: **

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

2 | 4 | 6 | 8 | |

3 | 4 | 5 | 6 |

- ANo
- BYes,
- CYes, 1
- DYes,
- EYes,

**Q8: **

True or False: A directly proportional relationship can always be represented by a straight line graph passing through the origin.

- AFalse
- BTrue

**Q10: **

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

- ANo
- BYes

**Q11: **

Given that , and when , find the value of .

- A
- B
- C
- D

**Q14: **

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

- A
- B
- C
- D
- E

**Q15: **

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)?

- A110 g/person
- B440 g/person
- C1,760 persons/g
- D1,760 g/person
- E110 persons/g

**Q16: **

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

Find the unit rate.

- A$60 per pizza
- B30ยข per pizza
- C15ยข per pizza
- D$15 per pizza
- E$30 per pizza

**Q18: **

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?

**Q19: **

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 |

- AYes,
- BYes,
- CNo

**Q21: **

If , then .

- A
- B
- C
- D

**Q23: **

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

**Q24: **

A website is selling e-books. It offers a discount of $0.50 for every referral you make. Is the amount of money saved by that offer directly proportional to the number of referrals you make?

- AYes
- BNo

**Q25: **

Olivia was giving away coupons for a free appetizer at a local restaurant. She gave away 52 coupons an hour. Is the number of coupons she gave away proportional to the number of hours that she worked?

- ANo
- BYes