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Type the correct answer in each box. Use numerals instead of words.

The domain of this function is [tex]\{-12, -6, 3, 15\}[/tex].

[tex]y = -\frac{2}{3}x + 7[/tex]

Complete the table based on the given domain.

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-6 & $\square$ \\
\hline
$\square$ & 5 \\
\hline
15 & $\square$ \\
\hline
$\square$ & 15 \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
To complete the table based on the given domain and function [tex]\( y = -\frac{2}{3} x + 7 \)[/tex], we have the following results:

1. For [tex]\( x = -6 \)[/tex]:
[tex]\[ y = -\frac{2}{3}(-6) + 7 = 4 + 7 = 11 \][/tex]

2. For [tex]\( y = 5 \)[/tex]:
Solving the equation for [tex]\( x \)[/tex]:
[tex]\[ 5 = -\frac{2}{3} x + 7 \][/tex]
[tex]\[ -\frac{2}{3} x = 5 - 7 \][/tex]
[tex]\[ -\frac{2}{3} x = -2 \][/tex]
[tex]\[ x = -2 \cdot \left( \frac{3}{-2} \right) = 3 \][/tex]

3. For [tex]\( x = 15 \)[/tex]:
[tex]\[ y = -\frac{2}{3}(15) + 7 = -10 + 7 = -3 \][/tex]

4. For [tex]\( y = 15 \)[/tex]:
Solving the equation for [tex]\( x \)[/tex]:
[tex]\[ 15 = -\frac{2}{3} x + 7 \][/tex]
[tex]\[ -\frac{2}{3} x = 15 - 7 \][/tex]
[tex]\[ -\frac{2}{3} x = 8 \][/tex]
[tex]\[ x = 8 \cdot \left( \frac{3}{-2} \right) = -12 \][/tex]

So, the completed table is:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-6 & 11 \\ \hline3 & 5 \\ \hline 15 & -3 \\ \hline-12 & 15 \\ \hline \end{tabular} \][/tex]

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