Solve the problem.
-The relationship between Celsius $\left( { } ^ { \circ } \mathrm { C } \right)$ and Fahrenheit $\left( { } ^ { \circ } \mathrm { F } \right)$ degrees of measuring temperature is linear. Find an equation relating ${ } ^ { \circ } \mathrm { C }$ and ${ } ^ { \circ } \mathrm { F }$ if $10 ^ { \circ } \mathrm { C }$ corresponds to $50 ^ { \circ } \mathrm { F }$ and $30 ^ { \circ } \mathrm { C }$ corresponds to $86 ^ { \circ } \mathrm { F }$. Use the equation to find the Celsius measure of $31 ^ { \circ } \mathrm { F }$.
A) $\mathrm { C } = \frac { 9 } { 5 } \mathrm {~F} - 80 ; - \frac { 121 } { 5 } \circ \mathrm { C }$
B) $\mathrm { C } = \frac { 5 } { 9 } \mathrm {~F} - \frac { 160 } { 9 } ; - \frac { 5 } { 9 } { } ^ { \circ } \mathrm { C }$
C) $C = \frac { 5 } { 9 } \mathrm {~F} - 10 ; \frac { 65 } { 9 } \circ \mathrm { C }$
D) $\mathrm { C } = \frac { 5 } { 9 } \mathrm {~F} + \frac { 160 } { 9 } ; 35 ^ { \circ } \mathrm { C }$

Question

Quizplus · Accepted Answer

The correct equation for converting Fahrenheit to Celsius is $C = \frac{5}{9}(F - 32)$. Given the points (50, 10) and (86, 30), we can find the slope and use one of the points to find the equation. The slope $m = \frac{30 - 10}{86 - 50} = \frac{20}{36} = \frac{5}{9}$. Using the point (50, 10), we can find the intercept $b$ such that $10 = \frac{5}{9}(50) + b$, solving for $b$ gives $b = -\frac{160}{9}$. Thus, the equation is $C = \frac{5}{9}F - \frac{160}{9}$. To find the Celsius temperature corresponding to $31^\circ F$, substitute $F = 31$ into the equation to get $C = \frac{5}{9}(31) - \frac{160}{9}$, which simplifies to $-\frac{5}{9}^\circ C$.

Solve the Problem (∘C)\left( { } ^ { \circ } \mathrm { C } \right)(∘C)

Solve the Problem $\left( { } ^ { \circ } \mathrm { C } \right)$