Find three ordered pair solutions by completing the table. Then use the ordered pairs to graph the equation.

[tex]\[ y = -4x - 3 \][/tex]

A.
\begin{tabular}{r|r}
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 0 & 3 \\
1 & -1 \\
-1 & 7
\end{tabular}

B.
\begin{tabular}{r|r}
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 0 & 0 \\
1 & 3 \\
-1 & -3
\end{tabular}

C.
\begin{tabular}{r|r}
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 0 & -3 \\
1 & 1 \\
-1 & -7
\end{tabular}

D.
\begin{tabular}{r|r}
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 0 & -3 \\
1 & -7 \\
-1 & 1
\end{tabular}



Answer :

To find ordered pair solutions for the given equation [tex]\( y = -4x - 3 \)[/tex], we need to substitute the [tex]\( x \)[/tex]-values into the equation to determine the corresponding [tex]\( y \)[/tex]-values. We then compare the completed pairs with those provided in the tables.

Let's go through the process step-by-step:

1. Given Equation: [tex]\( y = -4x - 3 \)[/tex]

2. Calculate [tex]\( y \)[/tex] for [tex]\( x = 0 \)[/tex]:
[tex]\[ y = -4(0) - 3 = -3 \][/tex]
So, the ordered pair is [tex]\((0, -3)\)[/tex].

3. Calculate [tex]\( y \)[/tex] for [tex]\( x = 1 \)[/tex]:
[tex]\[ y = -4(1) - 3 = -4 - 3 = -7 \][/tex]
So, the ordered pair is [tex]\((1, -7)\)[/tex].

4. Calculate [tex]\( y \)[/tex] for [tex]\( x = -1 \)[/tex]:
[tex]\[ y = -4(-1) - 3 = 4 - 3 = 1 \][/tex]
So, the ordered pair is [tex]\((-1, 1)\)[/tex].

From these calculations, we have the ordered pairs:
[tex]\[ (0, -3), (1, -7), (-1, 1) \][/tex]

Let's now review the tables to see which one matches these pairs.

Table A:
[tex]\[ \begin{array}{r|r} x & y \\ \hline 0 & 3 \\ 1 & -1 \\ -1 & 7 \\ \end{array} \][/tex]
- The first pair here is [tex]\((0, 3)\)[/tex], which does not match [tex]\((0, -3)\)[/tex].

Table B:
[tex]\[ \begin{array}{r|r} x & y \\ \hline 0 & 0 \\ 1 & 3 \\ -1 & -3 \\ \end{array} \][/tex]
- The first pair here is [tex]\((0, 0)\)[/tex], which does not match [tex]\((0, -3)\)[/tex].

Table C:
[tex]\[ \begin{array}{r|r} x & y \\ \hline 0 & -3 \\ 1 & 1 \\ -1 & -7 \\ \end{array} \][/tex]
- The second pair here is [tex]\((1, 1)\)[/tex], which does not match [tex]\((1, -7)\)[/tex].

Table D:
[tex]\[ \begin{array}{r|r} x & y \\ \hline 0 & -3 \\ 1 & -7 \\ -1 & 1 \\ \end{array} \][/tex]
- All pairs match: [tex]\((0, -3), (1, -7), (-1, 1)\)[/tex].

Therefore, the correct table is Table D.

To graph the equation [tex]\( y = -4x - 3 \)[/tex] using the ordered pairs, plot the points [tex]\((0, -3)\)[/tex], [tex]\((1, -7)\)[/tex], and [tex]\((-1, 1)\)[/tex] on a coordinate plane. Connect these points with a straight line, as [tex]\( y = -4x - 3 \)[/tex] is a linear equation.

Thus, the ordered pairs [tex]\((0, -3)\)[/tex], [tex]\((1, -7)\)[/tex], and [tex]\((-1, 1)\)[/tex] that match the equation [tex]\( y = -4x - 3 \)[/tex] correspond to Table D.