Directions: Write the linear equation in Standard Form. \( y=x-7 \) Incorrect Answer Given: \( x-y-7=0 \) Why is this incorrect? A) Answer fails to be in the form: B) Answer fails to make sure \( A, B, C \) are not fractions (or decimals). C) Answer fails to make sure \( A \) is positive.

To convert the equation \( y = x - 7 \) 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 it to get all terms on one side: \[ y - x + 7 = 0 \] or equivalently, \[ -x + y + 7 = 0 \] 2. To put it in standard form \( Ax + By = C \), we can multiply the entire equation by -1 to make \( A \) positive: \[ x - y - 7 = 0 \] or equivalently, \[ x - y = 7 \] Now, let's analyze the incorrect answer given, which is \( x - y - 7 = 0 \). The answer is incorrect because: A) The answer fails to be in the form: **This is incorrect.** The form \( x - y - 7 = 0 \) is indeed in the standard form \( Ax + By = C \). B) The answer fails to make sure \( A, B, C \) are not fractions (or decimals): **This is incorrect.** In the equation \( x - y - 7 = 0 \), \( A = 1\), \( B = -1\), and \( C = -7\) are all integers. C) The answer fails to make sure \( A \) is positive: **This is correct.** In the equation \( -x + y + 7 = 0 \), \( A = -1\), which is negative. The standard form requires \( A \) to be non-negative. Thus, the correct answer is **C**: The answer fails to make sure \( A \) is positive.