To convert the equation [tex]\( y - 3x = -14 \)[/tex] to function notation [tex]\( g(x) \)[/tex], we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
Here are the steps to do so:
1. Start with the given equation:
[tex]\[
y - 3x = -14
\][/tex]
2. Solve for [tex]\( y \)[/tex] by isolating it on one side of the equation. To do this, add [tex]\( 3x \)[/tex] to both sides of the equation:
[tex]\[
y - 3x + 3x = -14 + 3x
\][/tex]
Simplifying, we obtain:
[tex]\[
y = 3x - 14
\][/tex]
Now that we have [tex]\( y \)[/tex] expressed in terms of [tex]\( x \)[/tex], we can write the function notation [tex]\( g(x) \)[/tex]:
[tex]\[
g(x) = 3x - 14
\][/tex]
The correct function notation is [tex]\( g(x) = 3x - 14 \)[/tex], which corresponds to:
A. [tex]\( g(x) = 3x - 14 \)[/tex]
So, the correct answer is:
A. [tex]\( g(x) = 3x - 14 \)[/tex]
