Let’s start by solving the equation [tex]\(7x - y = 7\)[/tex] for each value of [tex]\(x\)[/tex] to complete the table.
We are given the equation:
[tex]\[7x - y = 7\][/tex]
We will solve for [tex]\(y\)[/tex] by isolating [tex]\(y\)[/tex] on one side of the equation:
[tex]\[ y = 7x - 7 \][/tex]
Now, let’s use this equation to find [tex]\(y\)[/tex] for each given value of [tex]\(x\)[/tex].
1. When [tex]\(x = 0\)[/tex]:
[tex]\[ y = 7(0) - 7 = -7 \][/tex]
2. When [tex]\(x = 1\)[/tex]:
[tex]\[ y = 7(1) - 7 = 0 \][/tex]
3. When [tex]\(x = 2\)[/tex]:
[tex]\[ y = 7(2) - 7 = 7 \][/tex]
4. When [tex]\(x = 3\)[/tex]:
[tex]\[ y = 7(3) - 7 = 14 \][/tex]
5. When [tex]\(x = 4\)[/tex]:
[tex]\[ y = 7(4) - 7 = 21 \][/tex]
So, we can fill in the table as follows (these values match the results above):
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$x$ & 0 & 1 & 2 & 3 & 4 \\
\hline
$y$ & -7 & 0 & 7 & 14 & 21 \\
\hline
\end{tabular}
\][/tex]
### Plotting the Points
Now, let’s plot the points [tex]\((x, y)\)[/tex] on a coordinate plane.
The points we need to plot are:
[tex]\[
(0, -7), (1, 0), (2, 7), (3, 14), (4, 21)
\][/tex]
### Graphing the Line
Once the points are plotted on the graph, draw a line through all of these points. This line represents the graph of the equation [tex]\(7x - y = 7\)[/tex].
### Conclusion
This completes the table and shows how to plot the points and graph the line for the equation [tex]\(7x - y = 7\)[/tex].
