A linearising transformation replaces the plotted coordinates by X,Y so the equation becomes Y=mX+c, with constant m,c. Multiplication or division can collect varying terms into one axis quantity. Write the required axes first. Rearrange the law using only valid operations. Identify gradient/intercept only after the equation is in Y=mX+c order; record restrictions from division. For y=ax2+bx, dividing by x 0 gives Y=y/x=aX+b with X=x. Alternatively Y=y/x2=bX+a with X=1/x. The constants exchange roles. Check: the original law may allow x=0, while a divided transformed graph does not contain that point.

A linearising transformation replaces the plotted coordinates by \(X,Y\) so the equation becomes \(Y=mX+c\), with constant \(m,c\). Multiplication or division can collect varying terms into one axis quantity.

Write the required axes first. Rearrange the law using only valid operations. Identify gradient/intercept only after the equation is in \(Y=mX+c\) order; record restrictions from division.

For \(y=ax^2+bx\), dividing by \(x\ne0\) gives \(Y=y/x=aX+b\) with \(X=x\). Alternatively \(Y=y/x^2=bX+a\) with \(X=1/x\). The constants exchange roles.

Check: the original law may allow \(x=0\), while a divided transformed graph does not contain that point.

Choosing algebraic transformed axes

Choosing algebraic transformed axes