Question

How to convert nonlinear equation to linear equation?

Answer 1

Let's take the non-linear equation:
${x}^{2} = \sqrt{3} y$
First Make The Equation To Be In Terms of Y

*Divide Both sides by
$\sqrt{3}$
$\frac{ {x}^{2} }{ \sqrt{3} } = \frac{ \sqrt{3} y}{ \sqrt{3} }$
*Simplify
$\frac{ {x}^{2} }{ \sqrt{3} } = y$
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
$\frac{ \sqrt{3} }{ {x}^{2} } = \frac{1}{y}$
A Linear Equation Takes The Format:
$y = mx + b$
So,
$\frac{1}{y} = y$
$b = 0$
$m(slope) = \frac{ \sqrt{3} }{x}$
$x = \frac{1}{x}$
Resulting in :
$\frac{1}{y} = \frac{ \sqrt{3} }{x} (\frac{1}{x} ) + 0$