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: 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. **Rearrange the equation**: \[ y = x + 5 \] Subtract \( x \) from both sides: \[ -x + y = 5 \] 2. **Standard Form**: The equation \( -x + y = 5 \) is in the form \( Ax + By = C \), where \( A = -1 \), \( B = 1 \), and \( C = 5 \). Now, let's analyze why the incorrect answer \( -x + y = 5 \) does not meet the standard form requirements: - **A must be positive**: In the equation \( -x + y = 5 \), \( A = -1 \), which is negative. In standard form, \( A \) should be a non-negative integer. To correct this, we can multiply the entire equation by -1 to make \( A \) positive: \[ -x + y = 5 \quad \text{(multiply by -1)} \] \[ x - y = -5 \] Now, we have the equation in standard form: \[ x - y = -5 \] In this case, \( A = 1 \), \( B = -1 \), and \( C = -5 \). Thus, the correct standard form of the equation \( y = x + 5 \) is: \[ x - y = -5 \] In summary, the original answer \( -x + y = 5 \) is incorrect because \( A \) is negative. The correct standard form should have \( A \) as a positive integer.