In an inverse proportion, when one quantity increases by a certain factor, the other quantity decreases by the same factor. Keep reading to see a real-life example of this situation.
Suppose x and y are variables and k is a constant. Then, y = 8x and y = -2x are examples of direct proportions. However, y = 3/x and y = -4/x are examples of inverse proportions. The figure above quickly shows the difference between direct proportion and inverse proportion.
A good real-life example of inverse proportion is the speed you drive and the time it takes to travel a certain distance. Suppose you need to drive to a city that is located 200 miles away.
The following table shows the time it will take you to get to your destination based on the speed.
|Speed (miles per hour)||Time|
|20 m/h||10 hours|
|40 m/h||5 hours|
|80 m/h||2.5 hours|
Did you make the following observations?
This means that every time you multiply the speed by 2, the time it takes to get to your destination is divided by 2 or multiplied by 1/2.
Furthermore, notice the following:
20 × 10 = 200
40 × 5 = 200
80 × 2.5 = 200
200 is a constant, so let k = 200.
20, 40, or 80 is the independent variable, so let x = 20, 40, or 80
10, 5, or 2.5 is the dependent variable, so let y = 10, 5, or 2.5
We get x × y = 200 or y = 200/x