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The line [tex][tex]$y = -2x - 8$[/tex][/tex] is graphed. Which ordered pairs are solutions to the equation? Check all that apply.

A. [tex][tex]$(-8, 8)$[/tex][/tex]
B. [tex][tex]$(-6, 2)$[/tex][/tex]
C. [tex][tex]$(-2, 4)$[/tex][/tex]
D. [tex][tex]$(0, -4)$[/tex][/tex]
E. [tex][tex]$(4, -12)$[/tex][/tex]

Sagot :

GinnyAnswer
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]
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