To write the given equation [tex]\( 9x + 3y = 12 \)[/tex] in function notation with [tex]\( x \)[/tex] as the independent variable, follow these steps:
1. Start with the given equation:
[tex]\[
9x + 3y = 12
\][/tex]
2. Isolate [tex]\( y \)[/tex] on one side of the equation. Start by subtracting [tex]\( 9x \)[/tex] from both sides:
[tex]\[
3y = 12 - 9x
\][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing every term by 3:
[tex]\[
y = \frac{12 - 9x}{3}
\][/tex]
4. Simplify the right-hand side:
[tex]\[
y = 4 - 3x
\][/tex]
This represents the function notation. To express this in the form [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = 4 - 3x
\][/tex]
Now, compare this with the given options:
- [tex]\( f(y) = -\frac{1}{3} y + \frac{4}{3} \)[/tex]
- [tex]\( f(x) = -3x + 4 \)[/tex]
- [tex]\( f(x) = -\frac{1}{3} x + \frac{4}{3} \)[/tex]
- [tex]\( f(y) = -3y + 4 \)[/tex]
The correct matching option is:
[tex]\[ f(x) = -3x + 4 \][/tex]
So, the function notation of the given equation is:
[tex]\[ f(x) = -3x + 4 \][/tex]
Therefore, among the provided options, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
