Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.