Recovering the Equation from a Straight Line

Find the gradient and intercept of the transformed graph, then match them to the original constants.

Here \(m=\dfrac{13-7}{5-2}=2\) and the vertical intercept gives \(c=3\), so the line is \(Y=2X+3\); substituting the axis expressions for \(Y\) and \(X\) recovers the original law.

Read both coordinates from the labelled transformed axes. Substitute them into Y = mX + c.

Use a second given relationship to find any remaining constant.

If the plotted axes do not start at zero, calculate the intercept; do not read the first visible point as the intercept.