In Mathematics and Physics, proportionality describes a linear relationship between two numbers or variables. If one quantity doubles in size, the other does as well; if one of the variables decreases, the other does as well. The symbol for proportionality resembles a stretched-out, lowercase Greek letter alpha.
Keep reading to know more about direct proportion, indirect proportion, and constant of proportionality.
Table of Contents
Significance and Examples of Constant of Proportionality
| Field | Example | Constant of Proportionality | Significance |
| Physics | Force and acceleration | Mass | Determines the force acting on an object in motion |
| Economics | Supply and demand | Elasticity | Indicates the responsiveness of the market to changes in price or quantity |
| Geometry | Similar figures | Ratio of corresponding sides | Remains constant, regardless of the size of the figures |
| Electricity | Ohm’s Law | Resistance | Determines how much current flows through a material for a given voltage |
| Cooking | Recipes | Ratio of ingredients | Determines how much of each ingredient is needed to make a recipe |
Proportionality
In Mathematics and Physics, We study quantities that rely on one another, and such values are said to as proportional to one another. In other words, if one variable or quantity varies, the other changes by a defined amount. This variable attribute is known as proportionality. There are two forms of variable proportionality. They are as follows:
- Directly Proportionality
- Inversely Proportionality
Direct Proportionality
Two quantities are said to be a direct proportion if one variable increases the other increases in the same proportion.
In other words, when the ratio between two variables x and y is a constant (x:y), two values x and y are directly proportional to each other (i.e. always remain the same). This means that x and y will either rise or decrease simultaneously by an amount that has no effect on the ratio. t is expressed numerically as y ∝ x.
Inverse Proportionality
When two quantities are inversely proportional, that is, when a rise in one quantity causes a reduction in the other and vice versa, they are said to be inversely proportional.
In other words, When the product of two variables x and y is a constant, they are inversely proportional to each other (always remain the same). This indicates that as x grows, y decreases, and vice versa, by an amount sufficient to keep xy constant. It is expressed numerically as y ∝ 1/x.
A simple example of inverse proportionality is the relation between speed and time to destination.
Speed and travel time are inversely linked because the quicker we go, the less time we take, i.e. the faster we travel, the less time we take.
Constant of Proportionality
The constant of proportionality is a constant value (often written as k) that relates two variables which are either in direct proportion or inverse proportion.
| Direct proportionality | Inverse proportionality |
| y ∝ x y=kx k = y/x | y ∝ 1/x y=k/x k=y.x |
Summary
- Directly proportional: When one amount increases, another amount increases at the same rate.
- Inversely Proportional: when one value decreases at the same rate that the other increases.
- The “constant of proportionality” is the value that relates two variables.
Frequently Asked Questions
1. What is triangle proportionality theorem?
The triangle proportionality theorem is a geometric statement that states that if you draw a line parallel to one side of a triangle, it will intersect and divide the other two sides correspondingly.
2. How do you find the constant of proportionality?
A constant of proportionality is a mathematical constant that is used to describe the relationship between two variables in a linear equation. For two variables x and y in direct proportionality with each other, the constant of proportionality is given as k=y/x. Similarly, for the inverse relation of variables x and y, the constant of proportionality is k=yx.
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