Question

The Fahrenheit temperature F and absolute temperature K satisfy a linear equation. Give that K = 273 when F=32 and that K=373 when F=212. Express K in terms of F and find the value of F, when K=0​

Answer 1

Answer ⇲

➽Assuming F along X-axis and K along Y-axis, we have two points (32, 273) and (212, 373) in xy-plane or FK-plane.

As F and K satisfy a linear equation. The equation of the line passing through (32, 273) and (212, 373) is

K−273=

212−32

373−273(F−32)

K−273=

180

100(F−32)

K=

9

5 (F−32)+273

Putting K=0, we get,

0=

9

5(F−32)+273

F −32= − 5

273×9

F=32−491.4=−459.4

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Answer 2

$\Large\sf{\underline{\underline{Question:-}}}$

The Fahrenheit temperature F and absolute temperature K satisfy a linear equation. Give that K=273 when F=32 and that K=373 when F=212. Express K in terms of F and find the value of F, when K=0

$\Large\sf{\underline{\underline{Answer:-}}}$

We know that simplest form of the equation of a line is y = mx + c .

Again assuming F along x-axis and K along y-axis, we can take equation in the form

K = mF + c ---------1

Equation 1 is satisfied by (32, 273) and (212, 373)

Therefore,

273 = 32m + c ------------2

and 373 = 212m + c ------------3

Solving (2) and (3), we get

m = $\Large\frac{5}{9}$

and c = $\Large\frac{2297}{9}$

Putting the values of m and c in (1), we get

K = $\Large\frac{5}{9} F + \frac{2297}{9}$

which is the required relation . When K = 0, (4) gives

$\large{\boxed{F = - 459.4}}$

$\pink{Hope \: it \: helps}$