To determine what the slope of the model represents, let's analyze the given data and its relationship between the independent and dependent variables.
Given:
- Independent variable (x-axis): Number of portions of fried shrimp.
- Dependent variable (y-axis): Number of grams of fat.
The data provided in the table:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{Number of portions} & 5 & 3 & 8 & 6 & 1 & 4 \\
\hline
\text{Number of grams of fat} & 45 & 27 & 72 & 54 & 9 & 36 \\
\hline
\end{array}
\][/tex]
In scatter plots that model a relationship between two variables, the slope of the line of best fit describes how the dependent variable changes with respect to the independent variable. Specifically, the slope ([tex]\( m \)[/tex]) represents the rate of change of the number of grams of fat per portion of fried shrimp.
This means for each additional portion of fried shrimp, the change in the number of grams of fat is constant.
Given the nature of the data: as the number of portions increases, the number of grams of fat increases proportionally. The value of the slope here would indicate how many grams of fat are contained in each portion of fried shrimp.
Thus, the slope of the model represents the number of grams of fat in each portion of fried shrimp.
Therefore, the correct answer is:
- The number of grams of fat in each portion of fried shrimp.
