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.
Algebraic conversions
| Given equation | Rearranged form | Plot (\(Y\) against \(X\)) | Gradient and intercept |
|---|---|---|---|
| \(y=ax^2+bx\) | \(\dfrac{y}{x}=ax+b\) | \(\dfrac{y}{x}\) against \(x\) | \(m=a\) \(c=b\) |
| \(y=ax^2+bx\) | \(\dfrac{y}{x^2}=b\left(\dfrac{1}{x}\right)+a\) | \(\dfrac{y}{x^2}\) against \(\dfrac{1}{x}\) | \(m=b\) \(c=a\) |
| \(y=a+\dfrac{b}{x}\) | \(y=b\left(\dfrac{1}{x}\right)+a\) | \(y\) against \(\dfrac{1}{x}\) | \(m=b\) \(c=a\) |
| \(y=ax+\dfrac{b}{x}\) | \(xy=ax^2+b\) | \(xy\) against \(x^2\) | \(m=a\) \(c=b\) |
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.
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