Question 3 (1 point) Directions: Write the linear equation in Standard Form. \( y=-\frac{5}{6} x-\frac{8}{3} \) Incorrect Answer Given: \( \frac{5}{6} x-y=-\frac{8}{3} \) Why is this incorrect? Answer fails to be in the form: Answer fails to make sure \( A, B, C \) are not fractions (or decimals). Answer fails to make sure \( A \) is positive.

The given incorrect answer, \( \frac{5}{6} x - y = -\frac{8}{3} \), is incorrect for several reasons: 1. **Not in Standard Form**: The standard form of a linear equation is \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) is positive. The given answer is not in this form because it has a fraction in the coefficient of \( x \) and does not have the constant term on the right-hand side. 2. **Fractions in Coefficients**: The standard form requires that \( A \), \( B \), and \( C \) are integers. The incorrect answer has a fraction, \( \frac{5}{6} \), in the coefficient of \( x \), which violates this requirement. 3. **Incorrect Sign for \( A \)**: The standard form requires that \( A \) (the coefficient of \( x \)) is positive. The incorrect answer has \( A \) as \( \frac{5}{6} \), which is positive, but it is not in its simplest form, and the original equation has \( A \) as \( -\frac{5}{6} \). To correct the equation and put it into standard form, we need to eliminate the fractions and ensure that \( A \) is positive. Here's how to do it: Given equation: \( y = -\frac{5}{6} x - \frac{8}{3} \) First, we can multiply every term by the least common multiple (LCM) of the denominators, which is 6, to eliminate the fractions: \( 6y = 6 \left( -\frac{5}{6} x \right) - 6 \left( \frac{8}{3} \right) \) This simplifies to: \( 6y = -5x - 16 \) Now, we can rearrange the terms to get the equation in standard form: \( 5x + 6y = -16 \) This is the correct standard form of the given equation, and it satisfies all the requirements: it has integer coefficients, \( A \) is positive, and it is in the form \( Ax + By = C \).