Let's solve for [tex]\( y \)[/tex] in the given equation [tex]\( x - y = -7 \)[/tex].
First, we rearrange the equation to solve for [tex]\( y \)[/tex]:
[tex]\[ x - y = -7 \][/tex]
[tex]\[ y = x + 7 \][/tex]
Now, we will complete the table by calculating the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & y = 0 + 7 = 7 \\
\hline
-7 & y = -7 + 7 = 0 \\
\hline
2 & y = 2 + 7 = 9 \\
\hline
1 & y = 1 + 7 = 8 \\
\hline
\end{array}
\][/tex]
So, the completed table looks like this:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
0 & 7 \\
\hline
-7 & 0 \\
\hline
2 & 9 \\
\hline
1 & 8 \\
\hline
\end{tabular}
\][/tex]
Next, let’s graph the equation [tex]\( x - y = -7 \)[/tex] or equivalently [tex]\( y = x + 7 \)[/tex] using the points from the table:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 7 \)[/tex]
- When [tex]\( x = -7 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 9 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 8 \)[/tex]
Plot these points on the coordinate plane and draw a straight line through them to graph the equation [tex]\( y = x + 7 \)[/tex]. The line will pass through the points (0,7), (-7,0), (2,9), and (1,8).
