Let's break down the problem step-by-step.
The equation given in the problem is [tex]\(y = 2 - 4x\)[/tex]. We need to fill in the missing [tex]\(y\)[/tex]-value in the table for [tex]\(x = -1\)[/tex]. Let's see how we can calculate the [tex]\(y\)[/tex]-values for the given [tex]\(x\)[/tex]-values and fill in the missing value.
1. When [tex]\(x = -2\)[/tex]:
[tex]\[
y = 2 - 4(-2) = 2 + 8 = 10
\][/tex]
So, [tex]\(y = 10\)[/tex].
2. When [tex]\(x = -1\)[/tex]:
[tex]\[
y = 2 - 4(-1) = 2 + 4 = 6
\][/tex]
So, [tex]\(y = 6\)[/tex].
3. When [tex]\(x = 0\)[/tex]:
[tex]\[
y = 2 - 4(0) = 2 - 0 = 2
\][/tex]
So, [tex]\(y = 2\)[/tex].
4. When [tex]\(x = 1\)[/tex]:
[tex]\[
y = 2 - 4(1) = 2 - 4 = -2
\][/tex]
So, [tex]\(y = -2\)[/tex].
5. When [tex]\(x = 2\)[/tex]:
[tex]\[
y = 2 - 4(2) = 2 - 8 = -6
\][/tex]
So, [tex]\(y = -6\)[/tex].
Now we have all the [tex]\(y\)[/tex]-values:
- [tex]\(x = -2\)[/tex], [tex]\(y = 10\)[/tex]
- [tex]\(x = -1\)[/tex], [tex]\(y = 6\)[/tex]
- [tex]\(x = 0\)[/tex], [tex]\(y = 2\)[/tex]
- [tex]\(x = 1\)[/tex], [tex]\(y = -2\)[/tex]
- [tex]\(x = 2\)[/tex], [tex]\(y = -6\)[/tex]
Here is the completed table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-2 & 10 \\
\hline
-1 & 6 \\
\hline
0 & 2 \\
\hline
1 & -2 \\
\hline
2 & -6 \\
\hline
\end{tabular}
\][/tex]
The specific missing [tex]\(y\)[/tex]-value for [tex]\(x = -1\)[/tex] is [tex]\(6\)[/tex].
