To determine what the slope of the model represents, let's analyze the problem step by step.
1. Understanding the Data and Scatter Plot:
- We have a set of values representing the number of portions of fried shrimp and the corresponding number of grams of fat.
- The data table is as follows:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Number of portions & 5 & 3 & 8 & 6 & 1 & 4 \\
\hline
Number of grams of fat & 45 & 27 & 72 & 54 & 9 & 36 \\
\hline
\end{tabular}
\][/tex]
2. Linear Relationship:
- The relationship between the number of portions [tex]\(x\)[/tex] and the number of grams of fat [tex]\(y\)[/tex] can be modeled using a simple linear regression equation of the form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
3. Interpreting the Slope:
- The slope [tex]\(m\)[/tex] indicates the rate of change of [tex]\(y\)[/tex] with respect to [tex]\(x\)[/tex]. In this context, it represents how many grams of fat change for each additional portion of fried shrimp.
4. Given the Slope Value:
- From the given answer, the slope [tex]\(m\)[/tex] has been determined to be [tex]\(9.000000000000002\)[/tex].
5. Conclusion:
- This value for the slope suggests that for each additional portion of fried shrimp, the amount of fat increases by 9 grams.
Therefore, the correct interpretation of the slope in this context is:
The number of grams of fat in each portion of fried shrimp.
Hence, the correct answer is:
The number of grams of fat in each portion of fried shrimp.
