Question

1. fahrenheit is a third temperature scale. plot the data in the table and use the graph to derive an equation for the relationship between the fahrenheit and celsius temperature scales.

example °c °f
melting point of selenium 221 430
boiling point of water 100 212
normal body temperature 37 98.6
freezing point of water 0 32
boiling point of chlorine -34.6 -30.2

Explanation:

Step1: Assume the linear - relationship

The relationship between Celsius ($C$) and Fahrenheit ($F$) is linear, and the general form of a linear equation is $F = mC + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Calculate the slope $m$

We can use two points from the table. Let's take the freezing - point of water $(C_1,F_1)=(0,32)$ and the boiling - point of water $(C_2,F_2)=(100,212)$. The slope formula is $m=\frac{F_2 - F_1}{C_2 - C_1}$.
$m=\frac{212 - 32}{100 - 0}=\frac{180}{100}=\frac{9}{5}$

Step3: Calculate the y - intercept $b$

We know that when $C = 0$, $F = 32$ from the point of the freezing - point of water. Substituting $C = 0$ and $F = 32$ into the equation $F=mC + b$, we get $32=\frac{9}{5}\times0 + b$, so $b = 32$.

Step4: Write the final equation

The equation relating Fahrenheit and Celsius is $F=\frac{9}{5}C+32$.

Answer:

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