Question

1. temperature the table below shows the temperature in fahrenheit for some corresponding temperatures in celsius.

celsius	fahrenheit
-10°	14°
0°	32°
10°	50°
20°	68°
30°	86°

a. write a formula for converting celsius temperatures to fahrenheit temperatures.

b. find the fahrenheit equivalents for 25°c and 35°c.

Explanation:

Step1: Assume linear relationship

Let the formula be $F = mC + b$, where $F$ is Fahrenheit temperature, $C$ is Celsius temperature.

Step2: Use two - point method

We know that when $C = 0$, $F = 32$ (from the table), so $32=m\times0 + b$, then $b = 32$.
When $C = 10$, $F = 50$. Substitute into $F=mC + b$: $50=m\times10+32$.
Solve for $m$:
\[

$$\begin{align*} 50&=10m + 32\\ 10m&=50 - 32\\ 10m&=18\\ m&=\frac{9}{5} \end{align*}$$

\]
So the formula is $F=\frac{9}{5}C + 32$.

Step3: Calculate for $C = 25$

Substitute $C = 25$ into $F=\frac{9}{5}C + 32$:
$F=\frac{9}{5}\times25+32=45 + 32=77$.

Step4: Calculate for $C = 35$

Substitute $C = 35$ into $F=\frac{9}{5}C + 32$:
$F=\frac{9}{5}\times35+32=63 + 32=95$.

Answer:

a. $F=\frac{9}{5}C + 32$
b. For $25^{\circ}C$, the Fahrenheit equivalent is $77^{\circ}F$. For $35^{\circ}C$, the Fahrenheit equivalent is $95^{\circ}F$.