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Sagot :
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.
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.
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