To complete the table for the given linear function [tex]\( y = -\frac{2}{3}x + 7 \)[/tex] and domain [tex]\( \{-12, -6, 3, 15\} \)[/tex]:
1. When [tex]\( x = -6 \)[/tex]:
Calculate [tex]\( y \)[/tex] when [tex]\( x = -6 \)[/tex].
Result: [tex]\( y = 11.0 \)[/tex]
2. When [tex]\( y = 5 \)[/tex]:
Find [tex]\( x \)[/tex] such that [tex]\( y = 5 \)[/tex].
Result: [tex]\( x = 3.0 \)[/tex]
3. When [tex]\( x = 15 \)[/tex]:
Calculate [tex]\( y \)[/tex] when [tex]\( x = 15 \)[/tex].
Result: [tex]\( y = -3.0 \)[/tex]
4. When [tex]\( y = 15 \)[/tex]:
Find [tex]\( x \)[/tex] such that [tex]\( y = 15 \)[/tex].
Result: [tex]\( x = -12.0 \)[/tex]
So, the completed table is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-6 & 11.0 \\
\hline
3.0 & 5 \\
\hline
15 & -3.0 \\
\hline
-12.0 & 15 \\
\hline
\end{tabular}
\][/tex]
