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 (0, 32). water freezes at 0°c or 32°f. the line also contains the point (-273.15, -459.67). absolute zero is at -273.15°c or -459.67°f. write the linear equation expressing fahrenheit temperature in terms of celsius temperature.
f = □

Explanation:

Step1: Find the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,32)$ and $(x_2,y_2)=(-273.15,-459.67)$. Then $m=\frac{-459.67 - 32}{-273.15-0}=\frac{-491.67}{-273.15}=\frac{9}{5}$.

Step2: Find the y - intercept $b$

We know the line passes through the point $(0,32)$. In the equation $F = mC + b$, when $C = 0$, $F=b$. So $b = 32$.

Step3: Write the linear equation

Substitute $m=\frac{9}{5}$ and $b = 32$ into $F=mC + b$. We get $F=\frac{9}{5}C+32$.

Answer:

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