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Question
The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C
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Solution
Assuming L along x-axis and C along y-axis, we have two points (124.942, 20) and (125.134, 110). By two point form, the point (L, C) satisfies the equation
`("C" - 20)/("L" - 124.942) = (110 - 20)/(125.134 - 124.942)`
= C - 20 = `90/0.192 ("L" - 124.942)`
= 0.192C - 3.84 = 90L - 11244.78
= 0.192(C - 20) + 11244.78 = 90 L
= `"L" = 0.192/90` (C - 20) + 124.942
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