Directions: Write the linear equation in Standard Form. \( y=\frac{3}{2} x+3 \) Incorrect Answer Given: \( -3 x+2 y=6 \) Why is this incorrect? Answer fails to be in the form: Ax \( +B y=C \) Answer fails to make sure \( A, B, C \) are not fractions (or decimals). Answer fails to make sure \( A \) is positive.

To convert the equation \( y = \frac{3}{2} x + 3 \) into standard form \( Ax + By = C \), we need to follow these steps: 1. **Eliminate the fraction**: Multiply the entire equation by 2 to eliminate the fraction: \[ 2y = 3x + 6 \] 2. **Rearrange to standard form**: Move all terms involving \( x \) and \( y \) to one side of the equation: \[ -3x + 2y = 6 \] Now, let's analyze the incorrect answer \( -3x + 2y = 6 \): - The equation is indeed in the form \( Ax + By = C \), where \( A = -3 \), \( B = 2 \), and \( C = 6 \). - However, the standard form requires that \( A \) be positive. Since \( A = -3 \) is negative, we need to multiply the entire equation by -1 to make \( A \) positive. 3. **Make \( A \) positive**: Multiply the equation by -1: \[ 3x - 2y = -6 \] Now, the equation \( 3x - 2y = -6 \) is in standard form with \( A = 3 \), \( B = -2 \), and \( C = -6 \), where \( A \) is positive. Thus, the correct standard form of the equation \( y = \frac{3}{2} x + 3 \) is: \[ 3x - 2y = -6 \]