Linear Law and Non-Linear Relations

6.2

Linear Law and Non-Linear Relations

Applying Linear Laws to Non-Linear Relationships

A non-linear equation can be reduced to linear form:
\(Y=mX+c\)
where \(Y\) and \(X\) are the functions of \(x\) and / or \(y\).
For example, given a non-linear equation \(y=x^2+1\), its linear form is \(Y=mX+c\), where \(Y=y\) and \(X=x^2\).

Example

Question

Convert the non-linear equation to linear form \(Y=mX+c\).

\(y=2px^2+qx\)

where \(p\) and \(q\) are constants.

Solution

Given the equation

\(y=2px^2+qx\).

To make the equation in the form of

\(Y=mX+c\),

We divide the given equation with \(x\).

\(\begin{aligned} (y&=2px^2+qx) \div x \\\\ \dfrac{y}{x}&=\dfrac{2px^2}{x}+\dfrac{qx}{x} \\\\ \dfrac{y}{x}&=2px+q. \end{aligned}\)