The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C.
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 $C$.

Solution:

It is given that when C = 20, the value of L is 124.942, whereas when C = 110, the value of L is 125.134.

Accordingly, points (20, 124.942) and (110, 125.134) satisfy the linear relation between L and C.

Now, assuming C along the x-axis and L along the y-axis, we have two points i.e., (20, 124.942) and (110, 125.134) in the XY plane.

Therefore, the linear relation between L and C is the equation of the line passing through points (20, 124.942) and (110, 125.134).

$(L-124.942)=\frac{125.134-124.942}{110-20}(C-20)$

$L-124.942=\frac{0.192}{90}(C-20)$

i.e., $\mathrm{L}=\frac{0.192}{90}(\mathrm{C}-20)+124.942$, which is the required linear relation

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