IDNLearn.com offers a unique blend of expert answers and community-driven insights. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.
Sagot :
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].
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].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.