| 6.2 |
Linear Law and Non-Linear Relations
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\(\blacksquare\) A non-linear equation can be reduced to linear form
\(Y=mX+c\)
where \(Y\) and \(X\) are the functions of
\(x\) and / or \(y\).
\(\blacksquare\) For example, given a non-linear equation \(y=x^2+1\),
its linear form is \(Y=mX+c\)
where \(Y=y\) and \(X=x^2\).
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Example:
Convert the non-linear equation to linear form \(Y=mX+c\).
\(y=2px^2+qx\)
where \(p\) and \(q\) are constants.
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Jawapan:
Given the equation
\(y=2px^2+qx\).
To make the equation in the form of
\(Y=mX+c\),
We divide the given equation with \(x\).
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\(\begin{aligned} (y&=2px^2+qx) \div x \\\\ \dfrac{y}{x}&=\dfrac{2px^2}{x}+\dfrac{qx}{x} \\\\ \dfrac{y}{x}&=2px+q. \end{aligned}\)
