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 1

Assuming C along the x-axis and L along the y-axis, we have two points, (20, 124.942) and (110, 125.134), in CL-plane.
As L is a linear function of C, the equation of the line passing through (20, 124.942) and (110, 125.134) is

$$\begin{gathered} L-124.942=\frac{125.134-124.942}{110-20}\left(C-20\right) \\ \Rightarrow L-124.942=\frac{0.192}{90}\left(C-20\right) \\ \Rightarrow L-124.942=\frac{0.032}{15}\left(C-20\right) \\ \Rightarrow L=\frac{0.032}{15}C+124.942-\frac{20\times 0.032}{15} \\ \Rightarrow L=\frac{0.032}{15}C+124.942-0.04267 \\ \Rightarrow L=\frac{4}{1875}C+124.899 \end{gathered}$$