To determine which ordered pairs are solutions to the equation [tex]\( y = -2x - 8 \)[/tex], we need to check each given ordered pair to see if it satisfies the equation. Let's evaluate each pair one by one.
1. Checking the pair [tex]\((-8, 8)\)[/tex]:
Substitute [tex]\( x = -8 \)[/tex] into the equation:
[tex]\[
y = -2(-8) - 8 = 16 - 8 = 8
\][/tex]
The resulting [tex]\( y \)[/tex] value is 8, which matches the [tex]\( y \)[/tex] coordinate of the pair [tex]\((-8, 8)\)[/tex]. So, [tex]\((-8, 8)\)[/tex] is a solution of the equation.
2. Checking the pair [tex]\((-6, 2)\)[/tex]:
Substitute [tex]\( x = -6 \)[/tex] into the equation:
[tex]\[
y = -2(-6) - 8 = 12 - 8 = 4
\][/tex]
The resulting [tex]\( y \)[/tex] value is 4, which does not match the [tex]\( y \)[/tex] coordinate of the pair [tex]\((-6, 2)\)[/tex]. So, [tex]\((-6, 2)\)[/tex] is not a solution of the equation.
3. Checking the pair [tex]\((-2, 4)\)[/tex]:
Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = -2(-2) - 8 = 4 - 8 = -4
\][/tex]
The resulting [tex]\( y \)[/tex] value is -4, which does not match the [tex]\( y \)[/tex] coordinate of the pair [tex]\((-2, 4)\)[/tex]. So, [tex]\((-2, 4)\)[/tex] is not a solution of the equation.
4. Checking the pair [tex]\((0, -4)\)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = -2(0) - 8 = 0 - 8 = -8
\][/tex]
The resulting [tex]\( y \)[/tex] value is -8, which does not match the [tex]\( y \)[/tex] coordinate of the pair [tex]\((0, -4)\)[/tex]. So, [tex]\((0, -4)\)[/tex] is not a solution of the equation.
5. Checking the pair [tex]\((4, -12)\)[/tex]:
Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
y = -2(4) - 8 = -8 - 8 = -16
\][/tex]
The resulting [tex]\( y \)[/tex] value is -16, which does not match the [tex]\( y \)[/tex] coordinate of the pair [tex]\((4, -12)\)[/tex]. So, [tex]\((4, -12)\)[/tex] is not a solution of the equation.
After checking all the pairs, the only ordered pair that satisfies the equation [tex]\( y = -2x - 8 \)[/tex] is [tex]\((-8, 8)\)[/tex].
Thus, the ordered pair that is a solution to the equation is:
[tex]\[ (-8, 8) \][/tex]
