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 $C$.
It is given that when $C = 20,$ the value of $L$ is $124.942,$ and when $C = 110,$ the value of $L$ is $125.134.$
Accordingly,the points $(20, 124.942)$ and $(110, 125.134)$ satisfy the linear relation between $L$ and $C.$
Using the two-point form of a line,$(L - L_1) = \frac{L_2 - L_1}{C_2 - C_1}(C - C_1),$ we substitute the given values:
$(L - 124.942) = \frac{125.134 - 124.942}{110 - 20}(C - 20)$
$(L - 124.942) = \frac{0.192}{90}(C - 20)$
$L = \frac{0.192}{90}(C - 20) + 124.942.$
Accordingly,the points $(20, 124.942)$ and $(110, 125.134)$ satisfy the linear relation between $L$ and $C.$
Using the two-point form of a line,$(L - L_1) = \frac{L_2 - L_1}{C_2 - C_1}(C - C_1),$ we substitute the given values:
$(L - 124.942) = \frac{125.134 - 124.942}{110 - 20}(C - 20)$
$(L - 124.942) = \frac{0.192}{90}(C - 20)$
$L = \frac{0.192}{90}(C - 20) + 124.942.$
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