Let's fill in the missing [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values using the equation:
[tex]\[ y = 2x + 1 \][/tex]
We will proceed step-by-step for each [tex]\( x \)[/tex]:
1. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 2(-1) + 1 = -2 + 1 = -1
\][/tex]
So, [tex]\( y = -1 \)[/tex].
2. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 2(0) + 1 = 0 + 1 = 1
\][/tex]
So, [tex]\( y = 1 \)[/tex].
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 2(1) + 1 = 2 + 1 = 3
\][/tex]
So, [tex]\( y = 3 \)[/tex].
4. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2(2) + 1 = 4 + 1 = 5
\][/tex]
So, [tex]\( y = 5 \)[/tex].
Now, we can fill in the values in the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-1 & -1 \\
\hline
0 & 1 \\
\hline
1 & 3 \\
\hline
2 & 5 \\
\hline
\end{tabular}
\][/tex]
So, the completed table is:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & -1 \\
\hline
0 & 1 \\
\hline
1 & 3 \\
\hline
2 & 5 \\
\hline
\end{array}
\][/tex]
