Answer :
To determine which table contains ordered pairs [tex]\((x, y)\)[/tex] that make the equation [tex]\( y = 2x + 4 \)[/tex] true, we'll check each table's pairs against the equation. Here's the step-by-step process:
### Table F
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 0 \\ \hline -1 & 6 \\ \hline 0 & 5 \\ \hline 1 & 6 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{True}) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{False, expected } 6) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{False, expected } 5) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{True}) \][/tex]
### Table H
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 0 \\ \hline -1 & 2 \\ \hline 0 & 4 \\ \hline 1 & 2 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{True}) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{True}) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{True}) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{False, expected } 2) \][/tex]
### Table G
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 8 \\ \hline -1 & 6 \\ \hline 0 & 4 \\ \hline 1 & 6 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{False, expected } 8) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{False, expected } 6) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{True}) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{True}) \][/tex]
### Last Table
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 0 \\ \hline -1 & 2 \\ \hline 0 & 4 \\ \hline 1 & 6 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{True}) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{True}) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{True}) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{True}) \][/tex]
### Conclusion
Only the last table contains all ordered pairs [tex]\((x, y)\)[/tex] that make the equation [tex]\( y = 2x + 4 \)[/tex] true.
### Table F
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 0 \\ \hline -1 & 6 \\ \hline 0 & 5 \\ \hline 1 & 6 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{True}) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{False, expected } 6) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{False, expected } 5) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{True}) \][/tex]
### Table H
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 0 \\ \hline -1 & 2 \\ \hline 0 & 4 \\ \hline 1 & 2 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{True}) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{True}) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{True}) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{False, expected } 2) \][/tex]
### Table G
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 8 \\ \hline -1 & 6 \\ \hline 0 & 4 \\ \hline 1 & 6 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{False, expected } 8) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{False, expected } 6) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{True}) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{True}) \][/tex]
### Last Table
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & 0 \\ \hline -1 & 2 \\ \hline 0 & 4 \\ \hline 1 & 6 \\ \hline \end{array} \][/tex]
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) + 4 = -4 + 4 = 0 \quad (\text{True}) \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 2(-1) + 4 = -2 + 4 = 2 \quad (\text{True}) \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 4 = 0 + 4 = 4 \quad (\text{True}) \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 2(1) + 4 = 2 + 4 = 6 \quad (\text{True}) \][/tex]
### Conclusion
Only the last table contains all ordered pairs [tex]\((x, y)\)[/tex] that make the equation [tex]\( y = 2x + 4 \)[/tex] true.
