Let's solve the given problem step-by-step.
We are given the equation [tex]\( y - 3x = -14 \)[/tex]. To express this equation in function notation [tex]\( g(x) \)[/tex], we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
1. Start with the given equation:
[tex]\[
y - 3x = -14
\][/tex]
2. To isolate [tex]\( y \)[/tex], add [tex]\( 3x \)[/tex] to both sides:
[tex]\[
y = 3x - 14
\][/tex]
Now, the equation is in the form [tex]\( y = g(x) \)[/tex], which represents the function in standard function notation.
Thus, we have:
[tex]\[
g(x) = 3x - 14
\][/tex]
Now, let's compare this with the choices given:
A. [tex]\( g(x) = 3x - 14 \)[/tex]
B. [tex]\( g(x) = -3x - 14 \)[/tex]
C. [tex]\( g(x) = 3x + 14 \)[/tex]
D. [tex]\( g(x) = -3x + 14 \)[/tex]
Clearly, the equation [tex]\( g(x) = 3x - 14 \)[/tex] matches option A.
Therefore, the correct answer is:
A. [tex]\( g(x) = 3x - 14 \)[/tex]
