To complete the table of ordered pairs for the given linear equation [tex]\( y = 2x - 14 \)[/tex], we need to determine the [tex]\( y \)[/tex] values for given [tex]\( x \)[/tex] values, and vice versa.
The table requires us to fill in the following values:
- [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex],
- [tex]\( x \)[/tex] when [tex]\( y = -6 \)[/tex],
- [tex]\( y \)[/tex] when [tex]\( x = 2 \)[/tex].
### Step-by-Step Solution
1. Calculate [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 2x - 14 \)[/tex]:
[tex]\[
y = 2(0) - 14 = -14
\][/tex]
So, [tex]\( y = -14 \)[/tex] when [tex]\( x = 0 \)[/tex].
2. Calculate [tex]\( x \)[/tex] when [tex]\( y = -6 \)[/tex]:
Substitute [tex]\( y = -6 \)[/tex] into the equation [tex]\( y = 2x - 14 \)[/tex]:
[tex]\[
-6 = 2x - 14
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
-6 + 14 = 2x
\][/tex]
[tex]\[
8 = 2x
\][/tex]
[tex]\[
x = \frac{8}{2} = 4
\][/tex]
So, [tex]\( x = 4 \)[/tex] when [tex]\( y = -6 \)[/tex].
3. Calculate [tex]\( y \)[/tex] when [tex]\( x = 2 \)[/tex]:
Substitute [tex]\( x = 2 \)[/tex] into the equation [tex]\( y = 2x - 14 \)[/tex]:
[tex]\[
y = 2(2) - 14 = 4 - 14 = -10
\][/tex]
So, [tex]\( y = -10 \)[/tex] when [tex]\( x = 2 \)[/tex].
### Fill in the Table
Based on the calculations, we can now complete the table as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & -14 \\
\hline
4 & -6 \\
\hline
2 & -10 \\
\hline
\end{array}
\][/tex]
So the completed table is:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & -14 \\
\hline
4 & -6 \\
\hline
2 & -10 \\
\hline
\end{array}
\][/tex]
