To determine which of the given points lies on the graph of the equation [tex]\( 8x + 2y = 24 \)[/tex], we need to check if each point satisfies the equation. We can do this by substituting the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values of each point into the equation and seeing if the equation holds true.
Let's evaluate each point one by one:
1. Point [tex]\((-1, 8)\)[/tex]:
[tex]\[
8(-1) + 2(8) = -8 + 16 = 8 \neq 24
\][/tex]
The point [tex]\((-1, 8)\)[/tex] does not satisfy the equation.
2. Point [tex]\((2, 8)\)[/tex]:
[tex]\[
8(2) + 2(8) = 16 + 16 = 32 \neq 24
\][/tex]
The point [tex]\((2, 8)\)[/tex] does not satisfy the equation.
3. Point [tex]\((6, -12)\)[/tex]:
[tex]\[
8(6) + 2(-12) = 48 - 24 = 24
\][/tex]
The point [tex]\((6, -12)\)[/tex] satisfies the equation.
4. Point [tex]\((8, 2)\)[/tex]:
[tex]\[
8(8) + 2(2) = 64 + 4 = 68 \neq 24
\][/tex]
The point [tex]\((8, 2)\)[/tex] does not satisfy the equation.
After evaluating all the points, we find that the point [tex]\((6, -12)\)[/tex] is the only one that satisfies the equation [tex]\( 8x + 2y = 24 \)[/tex]. Therefore, the point [tex]\((6, -12)\)[/tex] lies on the graph of the given equation.
