Question

How to convert nonlinear equation to linear equation?

Answer 1

Let's take the non-linear equation:

`{x}^(2) = √(3) y`
First Make The Equation To Be In Terms of Y

*Divide Both sides by

`√(3)`

`\frac{ {x}^(2) }{ √(3) } = ( √(3) y)/( √(3) )`
*Simplify

`\frac{ {x}^(2) }{ √(3) } = y`
You shouldn't keep a radical in the denominator, however we leave it for the purpose of the reciprocal.

*Take The Reciprocal Of Both Sides

`\frac{ √(3) }{ {x}^(2) } = (1)/(y)`
A Linear Equation Takes The Format:

`y = mx + b`
So,

`(1)/(y) = y`

`b = 0`

`m(slope) = ( √(3) )/(x)`

`x = (1)/(x)`
Resulting in :

`(1)/(y) = ( √(3) )/(x) ((1)/(x) ) + 0`