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[tex]\[
\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{\text{Freezing Temperatures} $\left( {}^\circ \right)$} \\
\hline F & C \\
\hline -13 & -25 \\
\hline -4 & -20 \\
\hline 5 & -15 \\
\hline 14 & -10 \\
\hline 23 & -5 \\
\hline
\end{tabular}
\][/tex]

The table shows temperatures below freezing measured in different units. Complete the equation in standard form to represent the relationship between [tex] F [/tex], a temperature measured in degrees Fahrenheit, and [tex] C [/tex], a temperature measured in degrees Celsius.

[tex]\[ 5F + \square C = 160 \][/tex]

[tex]\[ 39^\circ F = 3.9^\circ C \][/tex] rounded to the nearest tenth of a degree.

Answer :

To find the standard form equation that represents the relationship between Fahrenheit ([tex]\( F \)[/tex]) and Celsius ([tex]\( C \)[/tex]) using the provided table of values, we start with the equation [tex]\( 5F + \square C = 160 \)[/tex]. Our goal is to determine the missing coefficient that goes with [tex]\( C \)[/tex].

1. Understand the Relationship:
- We're given a few pairs of [tex]\( F \)[/tex] and [tex]\( C \)[/tex] values that show their linear relationship.
- This relationship can be expressed in the equation [tex]\( 5F + bC = 160 \)[/tex].

2. Choose a Pair:
- Let's choose the first pair from the table: [tex]\( F = -13 \)[/tex] and [tex]\( C = -25 \)[/tex].

3. Substitute in the Equation:
- Substitute these values into the equation to solve for [tex]\( b \)[/tex]:
[tex]\[
5(-13) + b(-25) = 160
\][/tex]

4. Calculate Step by Step:
- First, calculate [tex]\( 5 \times (-13) \)[/tex]:
[tex]\[
5 \times (-13) = -65
\][/tex]
- Substitute this into the equation:
[tex]\[
-65 + b(-25) = 160
\][/tex]
- Rearrange to solve for [tex]\( b \)[/tex]:
[tex]\[
b(-25) = 160 + 65
\][/tex]
[tex]\[
b(-25) = 225
\][/tex]
- Divide both sides by [tex]\(-25\)[/tex] to solve for [tex]\( b \)[/tex]:
[tex]\[
b = \frac{225}{-25} = -9
\][/tex]

5. Conclusion:
- The coefficient [tex]\( b \)[/tex] is [tex]\(-9\)[/tex].
- Therefore, the complete equation is:
[tex]\[
5F - 9C = 160
\][/tex]

This equation in standard form represents the relationship between Fahrenheit and Celsius using the given table of values.

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