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------------------------------------------------ A construction manager is monitoring the progress of the build of a new house. The scatterplot and table show the number of months since the start of the build and the percentage of the house still left to build. A linear function can be used to model this relationship.

New House

[tex]
\[
\begin{tabular}{|c|c|}
\hline
\text{Number of Months Since Start of Build, } x & \text{Percentage of House Left to Build, } y \\
\hline
0 & 100 \\
\hline
1 & 86 \\
\hline
2 & 65 \\
\hline
3 & 59 \\
\hline
4 & 41 \\
\hline
5 & 34 \\
\hline
\end{tabular}
\]
[/tex]

Which function best models the data?

A. [tex] y = -13.5x + 97.8 [/tex]

B. [tex] y = -13.5x + 7.3 [/tex]

C. [tex] y = 97.8x - 135 [/tex]

D. [tex] y = 7.3x - 97.8 [/tex]

To find the function that best models the data, we can determine the equation of the line that best fits the given data points using a linear function. The data points are:

- Months ([tex]$x$[/tex]): 0, 1, 2, 3, 4, 5
- Percentage left to build ([tex]$y$[/tex]): 100, 86, 65, 59, 41, 34

The goal is to check each provided linear function to see which one best matches the pattern of this data.

Let's verify the options:

1. [tex]$y = -135x + 97.8$[/tex]
2. [tex]$y = -13.5x + 7.3$[/tex]
3. [tex]$y = 97.8x - 135$[/tex]
4. [tex]$y = 7.3x - 97.8$[/tex]

Through analysis, we determine the following:

1. Slope and Intercept:

- Calculating the slope and intercept through a fitting process, we find:

- Slope (rate of change): Approximately -13.46
- Intercept (initial value when [tex]$x=0$[/tex]): Approximately 97.81

2. Matching with Functions:

- Option 1: The slope (-135) and intercept (97.8) clearly do not match our findings.
- Option 2: The slope (-13.5) is close to -13.46, but the intercept (7.3) is far from 97.81.
- Option 3: The slope (97.8) and intercept (-135) do not match our determined values.
- Option 4: The slope (7.3) and intercept (-97.8) do not match our findings.

Based on our findings, none of the options perfectly matches the calculated slope and intercept values from the data. If we round the slope to -13.5 and the intercept to 97.8, Option 2 might appear close in its slope value but is incorrect for the intercept.

Thus, none of the provided functions exactly model the calculated slope and intercept from the data.