Sure! Let's fill in the table by evaluating the function [tex]\( y = -2x - 4 \)[/tex] at the given values of [tex]\( x \)[/tex].
1. For [tex]\( x = -3 \)[/tex]:
- Substitute [tex]\( x = -3 \)[/tex] into the equation:
[tex]\[
y = -2(-3) - 4 = 6 - 4 = 2
\][/tex]
- So, [tex]\( y = 2 \)[/tex] when [tex]\( x = -3 \)[/tex].
2. For [tex]\( x = 0 \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = -2(0) - 4 = 0 - 4 = -4
\][/tex]
- So, [tex]\( y = -4 \)[/tex] when [tex]\( x = 0 \)[/tex].
3. For [tex]\( x = 3 \)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
y = -2(3) - 4 = -6 - 4 = -10
\][/tex]
- So, [tex]\( y = -10 \)[/tex] when [tex]\( x = 3 \)[/tex].
Now that we have evaluated the function for the given [tex]\( x \)[/tex]-values, we can fill in the table as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-6 & 0 \\
\hline
-3 & 2 \\
\hline
0 & -4 \\
\hline
3 & -10 \\
\hline
\end{tabular}
\][/tex]
