Principle of Proportionality
Introduction to principle of proportionality
In mathematics, two quantities are said to be proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.
The principle of Proportionality also refers to the equality of two ratios.
Proportionality is denoted by the symbol `oo`
Types of proportionality
Principle of Direct Proportionality
Let two variables x and y. If x varies directly proportional to y,
then those two variables can be expressed as, y `oo`
To remove the proportionality symbol, we introduce a constant "k" called as proportionality constant,
now the proportionality expression becomes, y = kx
Example problem to explain the principle of direct proportionality
If the value of y varies directly with the value of x and y = 8 when x = 2. Calculate the value of y when x = 12.
Given, y `oo`
So, y = kx
We know, y = 8 and x = 2. plug these values in the equation to find the value of k.
8 = 2k
k = 4
Now the equation becomes,
y = 4k
To find the value of y when x = 12,
plug k = 4 and x = 12 in y = kx
y = 4 * 12
y = 48
Principle of Inverse Proportionality
If two variables are inversely proportional to each other, say x and y.
`y` `oo` `1/x`
By introducing a proportionality constant, k
`y` = `k/x`
Example problem to explain the principle of inverse proportionality
If the value of y varies inversely with the value of x and y = 8 when x = 2. Calculate the value of y when x = 12.
We know the equation for inverse proportionality, `y` = `k/x`
Plug x = 2 and y = 8 in the equation to find the value of k,
8 = `k/2`
k = 16
Now the equation becomes, y = `16/x`
Now we have to find the value of y when x = 12.
Plug x = 12 in the above equation
y = `16/12`
y = `4/3`