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.
In general, with inverse proportion, when one quantity is multiplied by x, the other quantity is divided by x or multiplied by 1/x
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
In general, with inverse proportion, y = k/x and we say that y is inversely proportional to x.
Nov 18, 20 01:20 PM
Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.