To determine which of the given points lies on the graph of the equation \( 8x + 2y = 24 \), we will test each point by substituting \( x \) and \( y \) into the equation and checking if the equality holds.
Let's examine each point:
1. Point \((-1, 8)\)
[tex]\[
\begin{align*}
8x + 2y &= 8(-1) + 2(8) \\
&= -8 + 16 \\
&= 8
\end{align*}
\][/tex]
Since \( 8 \neq 24 \), the point \((-1, 8)\) does not lie on the graph of the equation.
2. Point \((2, 8)\)
[tex]\[
\begin{align*}
8x + 2y &= 8(2) + 2(8) \\
&= 16 + 16 \\
&= 32
\end{align*}
\][/tex]
Since \( 32 \neq 24 \), the point \((2, 8)\) does not lie on the graph of the equation.
3. Point \((6, -12)\)
[tex]\[
\begin{align*}
8x + 2y &= 8(6) + 2(-12) \\
&= 48 - 24 \\
&= 24
\end{align*}
\][/tex]
Since \( 24 = 24 \), the point \((6, -12)\) lies on the graph of the equation.
4. Point \((8, 2)\)
[tex]\[
\begin{align*}
8x + 2y &= 8(8) + 2(2) \\
&= 64 + 4 \\
&= 68
\end{align*}
\][/tex]
Since \( 68 \neq 24 \), the point \((8, 2)\) does not lie on the graph of the equation.
Therefore, the point [tex]\((6, -12)\)[/tex] is the one that lies on the graph of the equation [tex]\( 8x + 2y = 24 \)[/tex].
