To determine which table represents the same linear relationship as [tex]\( y = 2x - 5 \)[/tex], let's follow these steps for each table:
1. Table A:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
x & 0 & 2 & 4 \\
\hline
y & -5 & -1 & 3 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 0 \)[/tex]: [tex]\( y = 2(0) - 5 = -5 \)[/tex] (correct value)
- For [tex]\( x = 2 \)[/tex]: [tex]\( y = 2(2) - 5 = -1 \)[/tex] (correct value)
- For [tex]\( x = 4 \)[/tex]: [tex]\( y = 2(4) - 5 = 3 \)[/tex] (correct value)
2. Table B:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
x & 0 & 2 & 4 \\
\hline
y & -5 & 1 & 3 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 0 \)[/tex]: [tex]\( y = 2(0) - 5 = -5 \)[/tex] (correct value)
- For [tex]\( x = 2 \)[/tex]: [tex]\( y = 2(2) - 5 = -1 \)[/tex] (the table has [tex]\( y = 1 \)[/tex], incorrect value)
- For [tex]\( x = 4 \)[/tex]: [tex]\( y = 2(4) - 5 = 3 \)[/tex] (correct value)
3. Table C:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
x & 0 & 2 & 4 \\
\hline
y & 2 & -1 & 3 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 0 \)[/tex]: [tex]\( y = 2(0) - 5 = -5 \)[/tex] (the table has [tex]\( y = 2 \)[/tex], incorrect value)
- For [tex]\( x = 2 \)[/tex]: [tex]\( y = 2(2) - 5 = -1 \)[/tex] (correct value)
- For [tex]\( x = 4 \)[/tex]: [tex]\( y = 2(4) - 5 = 3 \)[/tex] (correct value)
4. Table D:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
x & 0 & 2 & 4 \\
\hline
y & 2 & 2 & 3 \\
\hline
\end{array}
\][/tex]
- For [tex]\( x = 0 \)[/tex]: [tex]\( y = 2(0) - 5 = -5 \)[/tex] (the table has [tex]\( y = 2 \)[/tex], incorrect value)
- For [tex]\( x = 2 \)[/tex]: [tex]\( y = 2(2) - 5 = -1 \)[/tex] (the table has [tex]\( y = 2 \)[/tex], incorrect value)
- For [tex]\( x = 4 \)[/tex]: [tex]\( y = 2(4) - 5 = 3 \)[/tex] (correct value)
By reviewing each table, we observe that only Table A accurately represents the same linear relationship as [tex]\( y = 2x - 5 \)[/tex] for all given [tex]\( x \)[/tex] values. Therefore, the correct table is:
[tex]\[
\boxed{\text{A}}
\][/tex]
