To complete the table using the rule [tex]\(2x - y = 4\)[/tex], we need to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex].
First, let's isolate [tex]\(y\)[/tex] in the given equation:
[tex]\[
2x - y = 4
\][/tex]
Adding [tex]\(y\)[/tex] to both sides gives:
[tex]\[
2x = y + 4
\][/tex]
Subtracting 4 from both sides, we get:
[tex]\[
y = 2x - 4
\][/tex]
Now we will use this equation to find the value of [tex]\(y\)[/tex] for each given [tex]\(x\)[/tex].
1. For [tex]\(x = 3\)[/tex]:
[tex]\[
y = 2(3) - 4 = 6 - 4 = 2
\][/tex]
2. For [tex]\(x = 4\)[/tex]:
[tex]\[
y = 2(4) - 4 = 8 - 4 = 4
\][/tex]
3. For [tex]\(x = 5\)[/tex]:
[tex]\[
y = 2(5) - 4 = 10 - 4 = 6
\][/tex]
4. For [tex]\(x = 25\)[/tex]:
[tex]\[
y = 2(25) - 4 = 50 - 4 = 46
\][/tex]
5. For [tex]\(x = 34\)[/tex]:
[tex]\[
y = 2(34) - 4 = 68 - 4 = 64
\][/tex]
Having calculated these values, we can now complete the table:
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
x & 3 & 4 & 5 & 25 & 34 \\
\hline
y & 2 & 4 & 6 & 46 & 64 \\
\hline
\end{tabular}
\][/tex]
