High School

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Rewrite the equation [tex]y - 31x = 93[/tex] as a function of [tex]x[/tex].

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]

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]

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Rewritten by : Barada