The graphical method is suitable only if there are exactly 2 variables. If the no . of variables are 3, constructing a 3-D graph is quite difficult to interpret . If the no. of constraints are more, the graph becomes a mess.
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The same,if you have accurate reading of measurement in graphical method you can precisely measure so there will be no error, in using analytical method you must have an exact & perfect calculation to have an perfect product. .
Alright, sweetheart, to verify the section formula by the graphical method, you'll need to draw a straight line and divide it at a certain ratio. Measure the lengths accurately, do some math, and if the ratios of the segments match the section formula, congratulations, you've verified it. Just make sure to dot your i's and cross your t's, darling.
M.C. Escher
graphical representations
Laplace will only generate an exact answer if initial conditions are provided