Sure! Let's analyze the provided data to determine the best-fitting function.
The data points given are:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & -3 \\
\hline
-5 & -4 \\
\hline
-4 & -5 \\
\hline
-3 & -6 \\
\hline
-2 & -7 \\
\hline
\end{array}
\][/tex]
To model this data, we look for a potential linear relationship [tex]\( y = mx + b \)[/tex].
The linear function is determined by the coefficients [tex]\( m \)[/tex] (slope) and [tex]\( b \)[/tex] (y-intercept). From the analysis:
The slope [tex]\( m = -1.0000000000000004 \approx -1 \)[/tex]
The intercept [tex]\( b = -8.999999999999998 \approx -9 \)[/tex]
Thus, the linear function that best models the data is:
[tex]\[
y = -1x - 9
\][/tex]
So, the function that models the data is:
[tex]\[
y = -x - 9
\][/tex]
