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Graphing Linear Equations by Plotting Points

Complete the table below for the equation [tex]y=-x+1[/tex]. Then use two of the ordered pairs to graph the equation.

[tex]\[
y = -x + 1
\][/tex]

\begin{tabular}{|c|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] & Ordered Pair \\
\hline
-2 & & \\
\hline
-1 & & \\
\hline
0 & & \\
\hline
1 & & \\
\hline
2 & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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].

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