Q. 121 - Precalculus Enhanced with Graphing Utilities

Question

The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F. Use the equation to find the Celsius measure of 70°F.

Step-by-Step Solution

Answer

Part (a) The linear equation relating °C and °F is: $F=\frac{9}{5}C+32$

Part (b) The Celsius measure of 70°F is: $21.1°C$

Part (a) Step 1. Given information

The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. 0°C corresponds to 32°F and 100°C corresponds to 212°F.  

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

Linear equation in slope-intercept form is: $y=mx+b$

For the given problem, it becomes: $F=mC+b$

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{212-32}{100-0}$

$m=\frac{180}{100}$

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

F-intercept, $b=32$

Substituting the values of slope and F-intercept in the linear equation, we get: $F=\frac{9}{5}C+32$

Part (b) Step 1. Using the linear equation to find the Celsius measure of 70°F

We have, $F=\frac{9}{5}C+32$

Put $F=70$ in the above equation

$70=\frac{9}{5}C+32$

$\frac{9}{5}C=70-32$

$C=\frac{5}{9}\times 38$

$C=\frac{190}{9}$

$C=21.1$