Question

the relationship between celsius temperature, c, and fahrenheit temperature, f, can be described by a linear equation in the form f = mc + b. the graph of this equation contains the point (-273.15, -459.67). absolute zero is at -273.15°c or -459.67°f. the line also contains the point (0, 32). water freezes at 0°c or 32°f. write the linear equation expressing fahrenheit temperature in terms of celsius temperature.
f = □

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, let $(x_1,y_1)=(-273.15,-459.67)$ and $(x_2,y_2)=(0,32)$. Then $m=\frac{32-(-459.67)}{0 - (-273.15)}$.

Step2: Calculate the slope

$m=\frac{32 + 459.67}{273.15}=\frac{491.67}{273.15}=1.8$.

Step3: Identify the y - intercept

The equation of a line is $F = mC + b$. The line passes through the point $(0,32)$. Substituting $C = 0$ and $F=32$ into $F = mC + b$, we get $b = 32$ (since when $C = 0$, $F=b$).

Step4: Write the linear equation

Substitute $m = 1.8$ and $b = 32$ into $F=mC + b$. The equation is $F=1.8C + 32$.

Answer:

$F = 1.8C+32$