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Straight Lines — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSStraight Lines2 Marks
Question
The Fahrenheit temperature F and absolute temperature K satisfy a linear equation. Given that K = 273 when F = 32 and that K = 373 when F = 212. Express K in terms of F and find the value of F, when K = 0
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Answer

Suppose that F along x-axis and K along y-axis, we have two points (32, 273) and (212, 373) in XY-plane. By two-point form, the point (F, K) satisfies the equation,then we get
$\mathrm{K}-273=\frac{373-273}{212-32}(\mathrm{F}-32)$ or $\mathrm{K}-273=\frac{100}{180}(\mathrm{F}-32)$
or $K=\frac{5}{9}(F-32)+273$ .......(1)
which is the required relation.
When K = 0, Equation (1) gives
$0=\frac{5}{9}(\mathrm{F}-32)+273$ or $\mathrm{F}-32=-\frac{273 \times 9}{5}=-491.4$ or F= -459.4

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