Miss Loi: In most Linear Law questions that come with a table of values, and with life in general, the so-called tough and critical part usually lies at the beginning - where you try every little trick you've learnt in your Algebra, Logarithms, Indices etc. chapters to twist and turn (like a Rubik's Cube) in order to die die manipulate a given grotesque equation (usually with two unknowns) into its 'linear' form: Y = mX + c, where m and c must be free of all variables from the original equation.

In this example, since there isn't any unknown or variable in the powers of our equation e.g. a^x, x^b+1 etc. we can rule out the method of 'logging both sides' and instead proceed with using algebraic manipulation (i.e. cross-multiplying) to form our Y = mX + c expression, like what you've done ...

A little table and graph to aid the reader

	0.0400	0.0100	0.0044	0.0025	0.0016	0.0011
	0.080	0.111	0.021	0.018	0.016	0.015

[Click Miss Loi's plotted masterpiece above to view it in its full glory]

Miss Loi's a little curious that you've selected as your X-axis since, as seen from the resultant graph, that inverse x² term is gonna lead to pretty small values of X that can be a little tricky to plot (and consequently slow you down during exam).

But in any case, all Linear Law students will pray for that magical moment when all that manipulating is finally validated, when they look up to the skies and thank the heavens upon seeing (most of) their constellation of plotted points for Y = mX + c align themselves on a straight line on the graph paper.

On the other hand, this moment may serve as a wake-up call for you to urgently re-examine your 'manipulation' workings if, to your horror, your 'constellation' resembles some random scatter diagram or the Crab Nebula.

So plotting against in this example, we find that 5 of the 6 points lie along a straight line (Rejoice!), with the 6th point (corresponding to x=10, y=0.9) being so far off the line that it belongs to a bird that obviously can't 'aim' well.

In such cases, your O-Level question will usually ask something like "It is suspected that an unusually large error occurs in one of the values of y. Identify the incorrect value and estimate its correct value."

For our question, it wasn't explicitly stated if the error, if indeed there's any, occurred in d or x and Miss Loi should have stated this in the question (sorry it's really been a busy week) to quell any big-time controversy of whether to leave out the 6th point entirely or draw a best-fit line through all 6 points.

But since it's pretty obvious that the 5 points lie almost perfectly on a straight line, we'll choose to ignore the 6th point since its abnormally-large distance from the line will affect the accuracy of estimating a and b if we choose to draw a best-fit line.

And so from your plotted graph above, we get the values of a and b as follows:

• Gradient:
• Y-intercept:

Hope everyone remembers the a little Quotient Rule in Differentiation: used here to differentiate our original equation i.e. (now that a and b are known) to obtain the value of x when d is at its maximum.