To convert the given equation [tex]\( y = -\frac{1}{3}x - 9 \)[/tex] into standard form [tex]\( Ax + By + C = 0 \)[/tex], follow these steps:
1. Multiply both sides by 3: This step is to eliminate the fraction. Multiplying each term by 3 gives:
[tex]\[
3y = -x - 27
\][/tex]
2. Rearrange the terms to fit standard form: In standard form, the equation should be in the format [tex]\( Ax + By + C = 0 \)[/tex]. This requires moving all terms to one side of the equation. Add [tex]\( x \)[/tex] to both sides:
[tex]\[
x + 3y = -27
\][/tex]
Thus, the equation in standard form is:
[tex]\[
x + 3y = -27
\][/tex]
Therefore, the correct answer is:
(D) [tex]\(\boxed{x + 3y = -27}\)[/tex]
