Writing an Inverse Variation Equation

Writing an Inverse Variation Equation

Writing an Inverse Variation Equation InteractivityAn inverse variation equation is an equation written in the form, y = k/x, where k represents the constant of proportionality. In this interactivity, you will learn how to write inverse variation equations and how to use them to solve practical problems. Click the player button to begin.

View a printable version of this interactivity.

 

 

Alternate Strategy

In the previous interactivity, you were presented one strategy to solve problems involving inverse variations. Below is a Self-Check that was included in the interactivity, along with an alternate strategy to determine the solution.

Problem: The amount of time needed to paint a room varies inversely with the number of painters working. If 3 painters completed a room in 75 minutes, how long would it have taken 5 painters to complete the same room?

Response: Given inverse variation {(x1 ,y1),(x2, y2)}, the following proportion is true: y2/y1= x1/x2. You can use this relationship to solve the practice problem.

3 painters completed a room in 75 minutes.

5 painters would complete the same room in ? minutes.

  minutes/minutes = painters/painters  

  x/75 = 3/5  

5 · x   = 75 · 3 Cross-multiply

  5x   = 225 Simplify

  x   = 45 Divide both sides by 5

Five painters would have completed the room in 45 minutes.

How to Identify an Inverse Variation Equation

Problem: Which equation represents an inverse variation?

  1. 4 = xy
  2. 4y = x

Response: Determine which equation can be written in the form y = k/x.

  1. View the solution below.
xy/x = 4/x
y = 4/x 
  1. View the solution below.
4y/4 = x/4
y = x/4 

Answer choice 1 represents an inverse variation.

 

Writing an Inverse Variation Equation Review

Self-Check IconWriting an Inverse Variation Equation Review InteractivityNow that you have learned how to write an inverse equation, it is time to test your knowledge. This interactivity will help you review the information covered throughout this topic. Click the player button to get started.

 

 

 

Digital Repository IconDid you answer the content review questions incorrectly? Do you want more instruction or extra practice? If so, view the video Representing an Inverse Variation Algebraically from eMediaVASM.