Lesson Worksheet: Inverse Variation Mathematics • 9th Grade

In this worksheet, we will practice creating formulas linking two quantities that vary directly and indirectly.


Decide if π‘₯ varies directly or inversely with 𝑦 and use this to find the value of 𝑦 when π‘₯=3.

  • A420
  • B3140
  • C1559
  • D4623


Which of the graphs shown represents inverse variation?

  • AB
  • BD
  • CC
  • DA


Which of the following relations represents an inverse variation between the two variables π‘₯ and 𝑦?

  • A𝑦=π‘₯+3
  • B𝑦=6π‘₯
  • Cπ‘₯𝑦=72
  • Dπ‘₯𝑦=14


𝑦 varies inversely with π‘₯. Given that 𝑦=8 when π‘₯=7, what is the constant of proportionality?


Given that 𝑦 varies inversely as π‘₯, write an equation for 𝑦 in terms of π‘₯ using π‘˜ as a non-zero constant.

  • A𝑦=π‘˜π‘₯
  • B𝑦=π‘˜π‘₯
  • C𝑦=π‘˜π‘₯
  • D𝑦=π‘˜π‘₯


Variable 𝑦 is inversely proportional to π‘₯. When π‘₯=3, 𝑦=6.

Find the value of 𝑦 when π‘₯=8.

  • A223
  • B8
  • C16
  • D113
  • E214


For a rectangle of fixed area, the length 𝑙 varies inversely with its width 𝑀. Given that 𝑙=22cm when 𝑀=16cm, determine the value of 𝑙 when 𝑀=44cm.


The number of hours 𝑛 needed for carrying out a certain task varies inversely with the number of workers who carry out the task. If the task is carried out by 23 workers in 35 hours, what is the time needed for 115 workers to carry out the task?


A copy center is printing leaflets for a local school. The time it takes for the job to be completed varies inversely with the number of copiers used, and if 4 copiers are used, the job will take 34 of an hour.

How many copiers are required to complete the job in half an hour?

Letting 𝑑 be the time in hours to complete the job using 𝑛 copiers, what is the value of the product, 𝑑𝑛?

Write an equation for 𝑑 in terms of 𝑛.

  • A𝑑=12𝑛
  • B𝑑=12𝑛
  • C𝑑=3𝑛
  • D𝑑=3𝑛
  • E𝑑=𝑛3


A group of scouts receives a donation of $1,000 to fund places on an international jamboree. The amount each scout receives for their trip varies inversely with the number of scouts from the group going to the jamboree.

Write an equation for π‘š, the amount each scout receives, in terms of 𝑛, the number of scouts from the group who are going to the jamboree.

  • Aπ‘š=100𝑛
  • Bπ‘š=1,000𝑛
  • Cπ‘š=10𝑛
  • Dπ‘š=𝑛1,000
  • Eπ‘š=𝑛100

If 25 scouts from the group are going to the jamboree, how much will each scout receive from the donation?

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