Inverse Proportion

An inverse proportion is a relationship between two quantities. As one quantity increases, the other decreases.

If y is inversely proportional x, we write y\propto \dfrac{1}{x} and the connecting equation is y=\dfrac{1}{x}, where k can be found using provided information.

The same four steps are required when dealing with inverse proportion:

  1. Write the proportion relationship.
  2. Convert to an equation using a constant of proportionality.
  3. Use given information to find the constant of proportionality.
  4. Substitute the constant of proportionality into the equation.


Suppose y is inversely proportional to \sqrt{x} and y=10, when x=25. Find the equation connecting x and y, then use it to find the value of y when x=100.

So, we have y\propto \dfrac{1}{\sqrt{x}}\Rightarrow y=\dfrac{k}{\sqrt{x}}

Using x=25, y=10 gives:


10=\dfrac{k}{5}\Rightarrow k=50

So, y=\dfrac{50}{\sqrt{x}} is the desired equation.

When x=100, y=\dfrac{50}{\sqrt{100}}

=\dfrac{50}{\pm 10}

=\pm 5


The value of a is inversely proportional to b. When a=4, b=10. We know that a=k/b, therefore 4=k/10. As a result, k=40. The final equation gives a=40/b.