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The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines3 Marks
Question
The length L (in centimeters) 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.
✓

Answer

$\text{L}_1=124.942, \text{C}_1=20 $$\text{L}_1=125.134,\text{C}_2=110$
Equation of line passing through
$(\text{L}_1,\text{C}_1)$ and $(\text{L}_2,\text{C}_2)$
$\text{L}-\text{L}_1=\Bigg(\frac{\text{L}_2-\text{L}_1}{\text{C}_2-\text{C}_1}\Bigg)\Big(\text{C}-\text{C}_1\Big)$
$\text{L}-124.942=\Big(\frac{125.134-124.942}{110-20}\Big)(\text{C}-20)$
$\text{L}-124.942=\frac{0.192}{90}(\text{C}-20)$
$\text{L}-124.92=\frac{192}{90000}(\text{C}-20)$
$\text{L}-124.942=\frac{4}{1875}(\text{C}-20)$
$\text{L}=\frac{4}{1875}\text{C}+124.942-4\times\frac{20}{1875}$
$\Rightarrow\text{L}=\frac{4}{1875}\text{C}+124.899$

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