Let's solve for the values of [tex]\( y \)[/tex] and fill in the [tex]\( y \)[/tex] values and ordered pairs for the equation [tex]\( y = -x + 1 \)[/tex] using the given [tex]\( x \)[/tex] values.
1. When [tex]\( x = -2 \)[/tex]:
[tex]\[
y = -(-2) + 1 = 2 + 1 = 3
\][/tex]
The ordered pair is [tex]\((-2, 3)\)[/tex].
2. When [tex]\( x = -1 \)[/tex]:
[tex]\[
y = -(-1) + 1 = 1 + 1 = 2
\][/tex]
The ordered pair is [tex]\((-1, 2)\)[/tex].
3. When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -(0) + 1 = 0 + 1 = 1
\][/tex]
The ordered pair is [tex]\((0, 1)\)[/tex].
4. When [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -(1) + 1 = -1 + 1 = 0
\][/tex]
The ordered pair is [tex]\((1, 0)\)[/tex].
5. When [tex]\( x = 2 \)[/tex]:
[tex]\[
y = -(2) + 1 = -2 + 1 = -1
\][/tex]
The ordered pair is [tex]\((2, -1)\)[/tex].
Let's fill in the table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
$x$ & $y$ & Ordered Pair \\
\hline
-2 & 3 & (-2, 3) \\
\hline
-1 & 2 & (-1, 2) \\
\hline
0 & 1 & (0, 1) \\
\hline
1 & 0 & (1, 0) \\
\hline
2 & -1 & (2, -1) \\
\hline
\end{tabular}
\][/tex]
Now, to graph the equation [tex]\( y = -x + 1 \)[/tex], you can plot the points [tex]\((-2, 3)\)[/tex], [tex]\((-1, 2)\)[/tex], [tex]\((0, 1)\)[/tex], [tex]\((1, 0)\)[/tex], and [tex]\((2, -1)\)[/tex] on a coordinate plane. Draw a line through these points, and you'll have the graph of the equation [tex]\( y = -x + 1 \)[/tex].
