Q. 122 - Precalculus Enhanced with Graphing Utilities

Question

The Kelvin (K) scale for measuring temperature is obtained by adding 273 to the Celsius temperature.

(a) Write a linear equation relating K and °C.

(b) Write a linear equation relating K and °F.

Step-by-Step Solution

Answer

Part (a) The linear equation relating K and °C is: $K=C+32$

Part (b) The linear equation relating K and °F is: $K=\frac{5}{9}(F-32)+273$

Part (a) Step 1. Given information

The Kelvin (K) scale for measuring temperature is obtained by adding 273 to the Celsius temperature.

Part (a) Step 2. Finding the linear equation relating K and Celsius (°C)

The required equation is: $K=C+273$

Part (b) Step 1. Finding the linear equation relating K and Fahrenheit (°F)

We have, $C=\frac{5}{9}(F-32)$ and $K=C+273$

Substituting for C in second equation, we get: $K=\frac{5}{9}(F-32)+273$