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.

Answer 1

Let the length be represented by $y$ and the temperature by $x$.

Then $(x_1,y_1)$ = (20, 124.942)

and $(x_2,y_2)$ = (110, 125.134)

Putting these values in

$y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)(x-x_1)$, we have

$\therefore y-124.942=\frac{(125.134-124.942)}{(110-20)}(x-20)$

$\Rightarrow y-124.942=\frac{0.192}{90}(x-20)$

$\Rightarrow y-124.942=\frac{0.032}{15}(x-20)$

$\Rightarrow 15y-1874.13=0.032x-0.64$

$\Rightarrow y=0.0021x+124.8993$ [Linear function of the form $y=mx+c$]

$\Rightarrow L=0.0021C+124.8993$