To determine which of the given points lies on the graph of the equation [tex]\(x - 2y = 6\)[/tex], we need to substitute each point into the equation and see if the equation holds true. Let's check each point one by one.
1. Point A: [tex]\((-2, 2)\)[/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex] into the equation:
[tex]\[
-2 - 2(2) = -2 - 4 = -6 \neq 6
\][/tex]
This point does not satisfy the equation.
2. Point B: [tex]\((-4, 2)\)[/tex]
Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 2\)[/tex] into the equation:
[tex]\[
-4 - 2(2) = -4 - 4 = -8 \neq 6
\][/tex]
This point does not satisfy the equation.
3. Point C: [tex]\((4, -2)\)[/tex]
Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = -2\)[/tex] into the equation:
[tex]\[
4 - 2(-2) = 4 + 4 = 8 \neq 6
\][/tex]
This point does not satisfy the equation.
4. Point D: [tex]\((2, -2)\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = -2\)[/tex] into the equation:
[tex]\[
2 - 2(-2) = 2 + 4 = 6 = 6
\][/tex]
This point satisfies the equation.
Therefore, the point that lies on the graph of [tex]\(x - 2y = 6\)[/tex] is:
[tex]\[
\boxed{(2, -2)}
\][/tex]
