Question

consider the function represented by $9x + 3y = 12$ with $x$ as the independent variable. how can this function be written using function notation?\
$\bigcirc\\ f(x)=-\frac{1}{3}y+\frac{4}{3}$\
$\bigcirc\\ f(x)=-3x + 4$\
$\bigcirc\\ f(x)=-\frac{1}{3}x+\frac{4}{3}$\
$\bigcirc\\ f(x)=-3y + 4$

Explanation:

Step1: Isolate the y-term

Subtract $9x$ from both sides.
$3y = 12 - 9x$

Step2: Solve for y

Divide all terms by 3.
$y = \frac{12}{3} - \frac{9x}{3} = 4 - 3x$

Step3: Rewrite in function notation

Since $x$ is independent, use $f(x)$.
$f(x) = -3x + 4$

Answer:

$f(x) = -3x + 4$ (matches the second option)