Question: Writing a Linear Model
Freezing Temperatures (°)
F
C
−13
−25
−4
−20
5
−15
14
−10
23
−5
The table shows temperatures below freezing measured in different units. Complete the equation in standard form to represent the relationship between $F$, a temperature measured in degrees Fahrenheit, and $C$, a temperature measured in degrees Celsius.
$5F + \frac{9}{5} C = -21.6$
$39^\circ F = [ ] ^\circ C$ rounded to the nearest tenth of a degree
1. **State the problem:** We are given a table of temperatures in Fahrenheit ($F$) and Celsius ($C$) below freezing and asked to complete the equation in standard form relating $F$ and $C$, and then convert $39^\circ F$ to Celsius.
2. **Given equation:**
$$5F + \frac{9}{5} C = -21.6$$
3. **Rewrite the equation in standard form:**
Multiply both sides by 5 to clear the fraction:
$$5 \times 5F + 5 \times \frac{9}{5} C = 5 \times (-21.6)$$
$$25F + 9C = -108$$
4. **Convert $39^\circ F$ to Celsius:**
Use the formula relating $F$ and $C$:
$$F = \frac{9}{5} C + 32$$
Rearranged to solve for $C$:
$$C = \frac{5}{9} (F - 32)$$
5. **Calculate $C$ when $F=39$:**
$$C = \frac{5}{9} (39 - 32) = \frac{5}{9} \times 7 = \frac{35}{9}$$
6. **Simplify and round:**
$$\frac{35}{9} \approx 3.888... \approx 3.9$$
**Final answer:**
$$39^\circ F = 3.9^\circ C$$