Answer :
To convert the equation [tex]\( y = -\frac{1}{3}x - 9 \)[/tex] into standard form, we need to follow specific steps:
1. Start with the given equation in slope-intercept form:
[tex]\[ y = -\frac{1}{3}x - 9 \][/tex]
2. The standard form of a linear equation is [tex]\( Ax + By = C \)[/tex], where [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are integers, and [tex]\( A \)[/tex] should be a non-negative integer.
3. To eliminate the fraction, multiply every term by 3 to clear the denominator:
[tex]\[ 3y = -x - 27 \][/tex]
4. Rearrange the equation to get all terms involving [tex]\( x \)[/tex] and [tex]\( y \)[/tex] on one side:
[tex]\[ x + 3y = -27 \][/tex]
This is now in the standard form [tex]\( Ax + By = C \)[/tex].
Thus, the correct answer is [tex]\( \boxed{D} \)[/tex].
1. Start with the given equation in slope-intercept form:
[tex]\[ y = -\frac{1}{3}x - 9 \][/tex]
2. The standard form of a linear equation is [tex]\( Ax + By = C \)[/tex], where [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are integers, and [tex]\( A \)[/tex] should be a non-negative integer.
3. To eliminate the fraction, multiply every term by 3 to clear the denominator:
[tex]\[ 3y = -x - 27 \][/tex]
4. Rearrange the equation to get all terms involving [tex]\( x \)[/tex] and [tex]\( y \)[/tex] on one side:
[tex]\[ x + 3y = -27 \][/tex]
This is now in the standard form [tex]\( Ax + By = C \)[/tex].
Thus, the correct answer is [tex]\( \boxed{D} \)[/tex].
