Let's fill in the table step-by-step based on the given domain and the information provided by the function [tex]\( y = -\frac{2}{3} x + 7 \)[/tex]:
1. For [tex]\( x = -6 \)[/tex]:
- Given [tex]\(-6\)[/tex], the corresponding [tex]\( y \)[/tex] value is 11.
2. For [tex]\( y = 5 \)[/tex]:
- Given [tex]\( y = 5 \)[/tex], the corresponding [tex]\( x \)[/tex] value is 3.
3. For [tex]\( x = 15 \)[/tex]:
- Given [tex]\( 15 \)[/tex], the corresponding [tex]\( y \)[/tex] value is -3.
4. For [tex]\( y = 15 \)[/tex]:
- Given [tex]\( y = 15 \)[/tex], the corresponding [tex]\( x \)[/tex] value is -12.
Thus, the completed table is:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-6 & 11 \\
\hline
3 & 5 \\
\hline
15 & -3 \\
\hline
-12 & 15 \\
\hline
\end{tabular}
