Solution: Assuming F along x-axis and K along y-axis, we have two points (32, 273)
and (212, 373) in XY-plane. By two-point form, the point (F, K) satisfies the equation
`K - 273 = (373 -273)/( 212-32) (F -32)` or `K- 273 = 100/180 (F- 32)`
or `K= 5/9 (F-32 ) +273` ..........(1)
which is the required relation.
When K = 0, Equation (1) gives
`0 = 5/9 (F-32 ) + 273 ` or `F-32 = - (273 xx 9)/5 = - 491.4` or `F= -459 .4`
`"Alternate"` method 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 =5/9` and ` c = 2297/9`
Putting the values of m and c in (1), we get
`k = 5/9 F + 2297/9 .................................(4)
which is the required relation. When K = 0, (4) gives F = – 459.4.
`color{blue} "Note"` We know, that the equation y = mx + c, contains two constants, namely, m and c. For finding these two constants, we need two conditions satisfied by the equation of line. In all the examples above, we are given two conditions to determine the equation of the line.