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    How do you work an approximation using linear interpolation?

    This is somewhat vague! Anyway, say you had (1, 4) (2, 9) and assumed a line between them you can work out y for any x. Either by inspection for example what is y when x = 3? Answer 14 by inspection.
    Or work out the equation of the line using the gradient of 5 \frac{y-4}{x-1}=5 \Rightarrow 5x-5=y-4 \Rightarrow y=5x-1 and now we could say what is y when x=27.5? Answer y=5 times 27.5 -1 = 136.5

    To summarise, linear interpolation is where you assume existing data has a linear relationship (y=mx+c) and use that relationship to work out other values. Technically, interpolation is where the values sought are within the range that you have data for and if not, it would be linear extrapolation.
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Updated: April 19, 2016
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