To answer the question in detail, let us:
1. Analyze the given data points for the candles.
2. Use this data to determine the function in slope-intercept form for the height of the smaller candle over time.
### Analyzing the Given Data Points
- Initial Height and Burning Rate:
- Taller Candle: Initial height = 16 cm, burns at a rate of 2.5 cm/hour.
- Smaller Candle: Initial height = 12 cm, burns at a rate of 1.5 cm/hour.
### Filling out the Table
Calculations for the Taller Candle:
- Height \( H_t \) at time \( h \):
\( H_t = 16 - 2.5h \)
Calculations for the Smaller Candle:
- Height \( H_s \) at time \( h \):
\( H_s = 12 - 1.5h \)
Using these equations, we can fill out the table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\textbf{Time (hours)} & \textbf{Taller Candle Height (cm)} & \textbf{Smaller Candle Height (cm)} \\
\hline
0 & 16 & 12 \\
\hline
1 & 13.5 & 10.5 \\
\hline
2 & 11 & 9 \\
\hline
3 & 8.5 & 7.5 \\
\hline
4 & 6 & 6 \\
\hline
5 & 3.5 & 4.5 \\
\hline
6 & 1 & 3 \\
\hline
7 & -1.5 & 1.5 \\
\hline
\end{tabular}
\][/tex]
### Identifying the Function for the Smaller Candle
The height of the smaller candle can be described by the linear equation \( S = 12 - 1.5h \), where \( S \) represents the height in centimeters and \( h \) represents the time in hours.
Given the provided options:
1. \( S = 12 - 1.5h \) (Correct)
2. \( S = -12 + 1.5h \)
3. \( S = 12 + 1.5h \)
4. \( S = -12 - 1.5h \)
The correct slope-intercept form equation for the height of the smaller candle is:
[tex]\[ \boxed{S = 12 - 1.5h} \][/tex]
