Answer :
To rewrite the equation [tex]\( y - 31x = 93 \)[/tex] as a function of [tex]\( x \)[/tex], follow these steps:
1. Start with the original equation:
[tex]\[
y - 31x = 93
\][/tex]
2. Isolate [tex]\( y \)[/tex]:
[tex]\[
y = 31x + 93
\][/tex]
This step involves adding [tex]\( 31x \)[/tex] to both sides of the equation to move the [tex]\( 31x \)[/tex] term to the right side.
3. Express [tex]\( y \)[/tex] as a function [tex]\( g(x) \)[/tex]:
[tex]\[
g(x) = 31x + 93
\][/tex]
Now we compare this result to the given options:
- A. [tex]\( g(x) = 93x + 31 \)[/tex]
- B. [tex]\( g(x) = 31x - 93 \)[/tex]
- C. [tex]\( g(x) = 31x + 93 \)[/tex]
- D. [tex]\( g(x) = -31x + 93 \)[/tex]
The correct function that the equation [tex]\( y - 31x = 93 \)[/tex] corresponds to is:
[tex]\[
g(x) = 31x + 93
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{C}
\][/tex]
1. Start with the original equation:
[tex]\[
y - 31x = 93
\][/tex]
2. Isolate [tex]\( y \)[/tex]:
[tex]\[
y = 31x + 93
\][/tex]
This step involves adding [tex]\( 31x \)[/tex] to both sides of the equation to move the [tex]\( 31x \)[/tex] term to the right side.
3. Express [tex]\( y \)[/tex] as a function [tex]\( g(x) \)[/tex]:
[tex]\[
g(x) = 31x + 93
\][/tex]
Now we compare this result to the given options:
- A. [tex]\( g(x) = 93x + 31 \)[/tex]
- B. [tex]\( g(x) = 31x - 93 \)[/tex]
- C. [tex]\( g(x) = 31x + 93 \)[/tex]
- D. [tex]\( g(x) = -31x + 93 \)[/tex]
The correct function that the equation [tex]\( y - 31x = 93 \)[/tex] corresponds to is:
[tex]\[
g(x) = 31x + 93
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{C}
\][/tex]
