Directions: Write the linear equation in Standard Form. \( y=x+8 \) Incorrect Answer Given: \( x=y-8 \) 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 decim:

To convert the equation \( y = x + 8 \) into standard form, we need to rearrange it into the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative. Starting with the given equation: 1. **Original equation**: \[ y = x + 8 \] 2. **Rearranging to standard form**: Subtract \( x \) from both sides: \[ -x + y = 8 \] 3. **Multiplying through by -1** (to make \( A \) positive): \[ x - y = -8 \] Now, we have the equation in standard form \( Ax + By = C \) where: - \( A = 1 \) - \( B = -1 \) - \( C = -8 \) Thus, the correct standard form of the equation is: \[ x - y = -8 \] ### Why the Incorrect Answer is Incorrect: The incorrect answer given was \( x = y - 8 \). This is not in standard form because: 1. It does not have the form \( Ax + By = C \). 2. It can be rearranged to \( x - y = -8 \), which is the correct standard form. Additionally, the incorrect answer does not ensure that \( A, B, C \) are integers in the required format. The standard form requires all coefficients to be integers, and the rearrangement to standard form is necessary to meet this requirement.