# Subject of a Formula

Till here we have learnt to form linear equations in one variable and formulae. Now, under this topic we will learn about subject of formula and how to change subject of a formula.

Subject of a Formula: Formula is an equation which is expressed in literals and variables using mathematical operators. Since a formula involves variables and constants in it. So, the variable part that we need to find out using the hints given in the question is known as subject of the equation.

For example, let us consider an equation from Newton’s Laws of Motion, i.e., v2 - u2 = 2as

Where v, u, a and s are final velocity, initial velocity, acceleration and displacement of the particle respectively.

This equation can be rearranged as:

s = $$\frac{v^{2} - u^{2}}{2a}$$, ‘s’ being the subject of the formula.

OR

a = $$\frac{v^{2} - u^{2}}{2s}$$, ‘a’ being the subject of the formula.

Changing the subject of the formula:

For changing the subject of the formula, the basic concept to be applied is that the variable to be found is kept on the right hand side of the equation and rest all the things are to be kept on the left hand side of the equation. If the given equation is not in the form of subject of the equation and is in the randomly arranged order, then the constants from left hand side is so eliminated that only the variable to be calculated is left on the right hand side and rest all constants are present on the right hand side and no variables are present on the right hand side.

For example, consider an equation:

s = ut + ½ at2, ‘s’ being the subject of the formula.

For ‘u’ to be the subject of the formula,

u = s/t - ½ at3

In this way we can change the subject of the formula.

Now, let’s see some examples on changing the subject of the formula:

1. The perimeter of a rectangle is twice the sum of its length and breadth.

Solution:

P = 2 (l + b)

Where, ‘P’ is the subject of the formula.

l = (P/2 - b), ‘l’ being the subject of the formula.

b = (P/2 – l), ‘b’ being the subject of the formula.

2. Change the subject of the given equation in terms of x:

z = 2x + 4y

Solution:

x = $$\frac{z – 4y}{2}$$

3. Change the subject of the equation in terms of y:

z = x2 + 2y +p

Solution:

y = $$\frac{z - x^{2} - p}{2}$$

In this way subject of equation can be changed from one vaiable to another.