To Linearize a non-linear equation involving two variables $x$ and $y$,
$Y = mX + c$.
Take note:
•	$Y$ can be a function of $x$ and/or $y$; similarly $X$ can be a function of $x$ and/or $y$.
•	$m$ and $c$ are constants and cannot contain $x$ or $y$.
•	There may be more than 1 way to linearize an equation.

Linearisation and Conversion to Linear Form

To Linearize a non-linear equation involving two variables $x$ and $y$,

•	$Y$ can be a function of $x$ and/or $y$; similarly $X$ can be a function of $x$ and/or $y$.

•	$m$ and $c$ are constants and cannot contain $x$ or $y$.

•	There may be more than 1 way to linearize an equation.

Divide or multiply both sides of the equation until it matches $Y=mX+c$: one variable expression on the left, a constant multiple of another variable expression plus a constant on the right.

$\dfrac{y}{x^2}=b\left(\dfrac{1}{x}\right)+a$

$\dfrac{y}{x^2}$ against $\dfrac{1}{x}$

More than one conversion can work for the same equation — the first two rows straighten the same law onto different axes. Always use the variables named on the axes in the question.

After converting, check the gradient and the intercept: if either still contains $x$ or $y$, the conversion is wrong.

Given equation	Rearranged form	Plot (\(Y\) against \(X\))	Gradient and intercept
\(y=ax^2+bx\)
\(y=ax^2+bx\)
\(y=a+\dfrac{b}{x}\)
\(y=ax+\dfrac{b}{x}\)

Linearization of Equations

Linearization of Equations