To complete the table for the graph given by the equation [tex]\(2x - y = 6\)[/tex], we need to find the values of [tex]\(y\)[/tex] that satisfy this equation for the given values of [tex]\(x\)[/tex].
Let's work through the calculation of [tex]\(y\)[/tex] step-by-step for each given [tex]\(x\)[/tex] value:
1. When [tex]\(x = -2\)[/tex]:
[tex]\[
2(-2) - y = 6
\][/tex]
Simplifying this,
[tex]\[
-4 - y = 6
\][/tex]
Adding 4 to both sides,
[tex]\[
-y = 10
\][/tex]
Multiplying both sides by -1,
[tex]\[
y = -10
\][/tex]
Thus, [tex]\(A = -10\)[/tex].
2. When [tex]\(x = -1\)[/tex]:
Given that [tex]\(y = -8\)[/tex], it does not need further calculation.
3. When [tex]\(x = 0\)[/tex]:
[tex]\[
2(0) - y = 6
\][/tex]
Simplifying this,
[tex]\[
0 - y = 6
\][/tex]
Multiplying both sides by -1,
[tex]\[
y = -6
\][/tex]
Thus, [tex]\(B = -6\)[/tex].
4. When [tex]\(x = 1\)[/tex]:
Given that [tex]\(y = -4\)[/tex], it does not need further calculation.
5. When [tex]\(x = 2\)[/tex]:
[tex]\[
2(2) - y = 6
\][/tex]
Simplifying this,
[tex]\[
4 - y = 6
\][/tex]
Subtracting 4 from both sides,
[tex]\[
-y = 2
\][/tex]
Multiplying both sides by -1,
[tex]\[
y = -2
\][/tex]
Thus, [tex]\(C = -2\)[/tex].
Hence, the completed table for the graph [tex]\(2x - y = 6\)[/tex] is:
[tex]\[
\begin{tabular}{c|c|c|c|c|c}
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & -10 & -8 & -6 & -4 & -2 \\
\end{tabular}
\][/tex]
