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= 13-75-2=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. Replace the axis symbols literally: if Y=y2, X=x3, then Y=mX+c means y2=mx3+c. If Y= e2y, X=x2, it means e2y=mx2+c. If Y=y3, X=ln x, it means y3=mln x+c, with x>0.