To determine which of the given points [tex]\((x, y)\)[/tex] lies on the graph of the equation [tex]\(8x + 2y = 24\)[/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 [tex]\((-1, 8)\)[/tex]:
[tex]\[
8(-1) + 2(8) = -8 + 16 = 8
\][/tex]
This does not equal 24, so [tex]\((-1, 8)\)[/tex] does not lie on the graph.
2. Point [tex]\((2, 8)\)[/tex]:
[tex]\[
8(2) + 2(8) = 16 + 16 = 32
\][/tex]
This does not equal 24, so [tex]\((2, 8)\)[/tex] does not lie on the graph.
3. Point [tex]\((6, -12)\)[/tex]:
[tex]\[
8(6) + 2(-12) = 48 - 24 = 24
\][/tex]
This equals 24, so [tex]\((6, -12)\)[/tex] lies on the graph.
4. Point [tex]\((8, 2)\)[/tex]:
[tex]\[
8(8) + 2(2) = 64 + 4 = 68
\][/tex]
This does not equal 24, so [tex]\((8, 2)\)[/tex] does not lie on the graph.
Therefore, the point that lies on the graph of [tex]\(8x + 2y = 24\)[/tex] is [tex]\((6, -12)\)[/tex].
