To convert the given equation [tex]\( y = -\frac{1}{3} x + \frac{23}{9} \)[/tex] into standard form, follow these steps:
1. Identify the given slope-intercept form equation:
[tex]\[
y = -\frac{1}{3}x + \frac{23}{9}
\][/tex]
2. Eliminate the fractions:
Multiply every term by the least common multiple (LCM) of the denominators (which is 9 in this case) to eliminate the fractions.
[tex]\[
9 \cdot y = 9 \cdot \left( -\frac{1}{3}x \right) + 9 \cdot \frac{23}{9}
\][/tex]
Simplifying each term, we get:
[tex]\[
9y = -3x + 23
\][/tex]
3. Rearrange into Standard Form [tex]\( Ax + By = C \)[/tex]:
Move all terms to one side of the equation to arrange them into the standard form:
[tex]\[
3x + 9y = 23
\][/tex]
Therefore, the standard form of the equation is:
[tex]\[ \boxed{3x + 9y = 23} \][/tex]
Typed without spaces and all in lowercase would be:
[tex]\[ 3x+9y=23 \][/tex]
The correct answer is:
[tex]\[ \boxed{a} \][/tex]
