Lesson Worksheet: Graphs of Direct and Inverse Variations Mathematics

In this worksheet, we will practice drawing and interpreting nonlinear graphs in order to solve problems.


The given table shows how 𝑦 varies with 𝑥.


Which of the following graphs represents the relation between 𝑥 and 𝑦?

  • A
  • B
  • C
  • D
  • E


The given table shows how 𝑦 varies with 𝑥.


Which of the following graphs represents the relation between 𝑥 and 𝑦?

  • A
  • B
  • C
  • D
  • E


Considering the following graph of 𝑥 and 𝑦, explain what happens to 𝑦 as 𝑥 increases.

  • AAs 𝑥 increases, 𝑦 decreases and then increases.
  • BAs 𝑥 increases, 𝑦 increases and then decreases.
  • CAs 𝑥 increases, 𝑦 increases.
  • DAs 𝑥 increases, 𝑦 decreases.
  • EAs 𝑥 increases, 𝑦 remains constant.


The following graph shows the distance a particle travels as time goes by.

What was the distance the particle traveled after 10 seconds?

How long did it take the particle to travel a distance of 18 meters?


A group of workers are going to build a small building. The following graph shows the relation between the number of workers and the average hours required to complete the building.

How many hours will it take if there are 12 workers to build the building?

How many workers are needed to finish the building in 15 hours?


The relation between the electric current 𝐼 in a conductor and its resistance 𝑅 when the applied voltage is fixed is represented by the given graph.

What is the value of the electric current when the resistance is equal to 2 ‏Ω?

What is the value of the resistance if the electric current is equal to 4 A?


The time, 𝑡, needed to reach a certain destination is inversely proportional to the moving speed, 𝑣. The following curve is a graphical representation of this relation. Find the moving speed needed to reach a destination in 7 hours.


Imagine that you are an engineer designing a race car and you want to know how steep a turn the car can make. The following graph represents the relation between the friction force needed, 𝐹, and the radius of the turn, 𝑅. Determine the minimum turn radius that can be achieved if the maximum friction force that can be provided by the car is equal to 7‎ ‎000 N.

Racing car taking a tight turn


The volume of a gas 𝑉 is inversely proportional to its pressure 𝑝 when the temperature is constant, as shown in the given graph. What is the volume of the gas when the pressure is equal to 1,600 pascals?

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