Directions: Write the linear equation in Standard Form. \( y=x+5 \) Incorrect Answer Given: \( -x+y=5 \) 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.

To convert the equation \( y = x + 5 \) 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**: \[ y = x + 5 \] 2. **Rearranging to standard form**: Subtract \( x \) from both sides: \[ -x + y = 5 \] 3. **Standard form**: The equation \( -x + y = 5 \) is indeed in the form \( Ax + By = C \), but it does not meet the requirement that \( A \) should be positive. To make \( A \) positive, we can multiply the entire equation by -1: \[ x - y = -5 \] Now, we have: \[ 1x - 1y = -5 \] In this case, \( A = 1 \), \( B = -1 \), and \( C = -5 \). Thus, the correct standard form of the equation is: \[ x - y = -5 \] ### Summary of why the original answer was incorrect: - The original answer \( -x + y = 5 \) is in standard form but does not have \( A \) as a positive integer. - The correct standard form should have \( A \) positive, which we achieved by multiplying the entire equation by -1.