Directions: Write the linear equation in Standard Form. $$ y=-\frac{1}{3} x+\frac{23}{9} $$ Incorrect Answer Given: $$ -\frac{1}{3} x-y=-\frac{23}{9} $$ Why is this incorrect? Answer fails to be in the form: $$ A x+B y=C $$ Answer fails to make sure $$ A, B, C $$ are not fractions (or decimals). Answer fails to make sure $$ A $$ is positive.

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To convert $$ y = -\frac{1}{3} x + \frac{23}{9} $$ to standard form, multiply by 9 to get $$ 3x + 9y = 23 $$. The incorrect answer has fractions and does not meet the standard form criteria. To convert the equation $$ y = -\frac{1}{3} x + \frac{23}{9} $$ into standard form $$ Ax + By = C $$, we need to follow these steps: 1. **Eliminate the fraction**: We can multiply the entire equation by a common denominator to eliminate the fractions. The denominators in the equation are 3 and 9, and the least common multiple is 9. 2. **Multiply through by 9**: $$ 9y = 9\left(-\frac{1}{3} x\right) + 9\left(\frac{23}{9}\right) $$ This simplifies to: $$ 9y = -3x + 23 $$ 3. **Rearrange to standard form**: We want to get all terms on one side of the equation: $$ 3x + 9y = 23 $$ 4. **Ensure $$ A $$ is positive**: In this case, $$ A = 3 $$, which is already positive. Now, the equation $$ 3x + 9y = 23 $$ is in standard form $$ Ax + By = C $$ where $$ A = 3 $$, $$ B = 9 $$, and $$ C = 23 $$. Thus, the correct standard form of the equation is: $$ 3x + 9y = 23 $$ The incorrect answer given, $$ -\frac{1}{3} x - y = -\frac{23}{9} $$, is not in standard form because it has fractions and does not have $$ A $$ as a positive integer.

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