Math by Grades Math by Topics Math Worksheets Math for Specific Tests Math Fun and Games Exam Preparation Math in Video Lessons Science Others
Inverse Variation
There are many situations in our daily lives that involve inverse variation (indirect variation).
For example, the number of days required to build a bridge is varies inversely to the number of workers. As the number of workers increases, the number of days required to build would decrease.
In general, when two variables x and y are such that
xy = k where k is a non-zero constant, we say that y varies inversely with x.
In notation, inverse variation is written as
Example:
Suppose that y varies inversely as x and that y = 8 when x = 3.
a) Form an equation connecting x and y.
b) Calculate the value of y when x = 10.
Solution:
i.e. xy = k where k is a non-zero constant
a) Substitute x = 3 and y = 8 into the equation to obtain k
3 × 8 = k ⇒ k = 24
The equation is xy = 24
b) When x = 10, 10 × y = 24 ⇒ y =
Example:
Suppose that y varies inversely as x 2 and that y = 10 when x = .
a) Find the equation connecting x and y .
b) Find the value of y when x = 3.
Solution:
i.e. yx2 = k
a) Substitute x = and y = 10 into the equation to obtain k
The equation is yx2 =
b) When x = 3,
The following video gives some practical examples of direct variation and indirect/inverse variation.
Custom Search
We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.