Question

The Fahrenheit temperature $F$ and absolute temperature $K$ satisfy a linear equation. Given that $K = 273$ when $F = 32$ and that $K = 373$ when $F = 212$.
Find the value of $F$, when $K = 0$.

• A. $459.4$
• B. $-459.4$
• C. $287.3$
• D. $-287.3$

Answer 1

Answer: (B)

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
$K-273=\frac{373-273}{212-32}\left(F-32\right)$
or $K=\frac{5}{9}\left(F-32\right)+273\quad\ldots\left(i\right)$
When $K = 0$, equation $\left(i\right)$ gives $0=\frac{5}{9}\left(F-32\right)+273$
or $F-32=-\frac{273\times9}{5}$ or $F=-459.4$