What does it mean to be inversely proportional?

Answer 1

I will use Ideal Gas Law to illustrate the meanings of " inversely proportional " and of " proportional to".

The Ideal Gas Law is commonly written as follows :

PV = nRT

P = absolute pressure

V = volume occupied by the gas

n = moles of the gas

R = universal gas constant

T = absolute temperature

This equation may be re-arranged giving :

V = nRT / P

For a fixed amount number of moles of gas at a fixed temperature , you have :

V = ( nRT ) / P = K / P

where K is a constant determined by the fixed n, R, and T. The equation indicates that the volume occupied, V , is inversely proportional to the absolute pressure, P. The equation also indicates that

the product, PV , is constant.

( 1 ) Multiplying the absolute pressure, P , by a factor of 2 would divide the volume occupied by 2.

( 2 ) Multiplying the absolute pressure, P , by a factor of G would divide the volume occupied by G.

The Ideal Gas Law also gives :

P = nRT / V

For ideal gas moles and volume fixed, you get :

P = ( nR/ V ) ( T ) = ( K ) ( T )

In this situation, the absolute pressure, P , is directly proportional to the absolute temperature , T .

( 1 ) Heating or cooling a fixed amount of gas in a closed and rigid container gives the absolute

pressure, P , directly proportional to the absolute temperature, T.

( 2 ) Changing the absolute temperature from 300 K to 600 K would double the absolute pressure,

P , exerted by the gas.

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In math, two variables are proportional if a change in one is always accompanies a change in the other, and if the changes are always related by a constant multiplier.

You can contrast the concept of inverse proportionalityagainst direct proportionality. If your variables are "inversely proportional" to each other and all other variables remain constant, the magnitude or absolute value of one inversely proportional variable will decrease if the other variable increases, while their product remains the same.

Source: Wikipedia

Answer 2

It means that the multiplication of the two parameters is constant.