Directions: Write the linear equation in Standard Form. \( y=-\frac{2}{7} x-\frac{11}{7} \) Incorrect Answer Given: \( \frac{2}{7} x+y=-\frac{11}{7} \) 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 \( y = -\frac{2}{7} x - \frac{11}{7} \) into standard form, we need to rearrange it into the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) is positive. Starting with the given equation: \[ y = -\frac{2}{7} x - \frac{11}{7} \] 1. **Eliminate the fraction**: To eliminate the fractions, we can multiply the entire equation by 7 (the denominator of the fractions): \[ 7y = 7 \left(-\frac{2}{7} x\right) + 7 \left(-\frac{11}{7}\right) \] This simplifies to: \[ 7y = -2x - 11 \] 2. **Rearrange to standard form**: Now, we want to rearrange this equation into the standard form \( Ax + By = C \): \[ 2x + 7y = -11 \] 3. **Ensure \( A \) is positive**: In this case, \( A = 2 \), which is already positive. Thus, the final standard form of the equation is: \[ 2x + 7y = -11 \] ### Why the Incorrect Answer is Incorrect: The incorrect answer given was \( \frac{2}{7} x + y = -\frac{11}{7} \). This is incorrect for the following reasons: 1. **Not in standard form**: The equation is not in the form \( Ax + By = C \) with integer coefficients. 2. **Fractions present**: The coefficients \( \frac{2}{7} \) and \( -\frac{11}{7} \) are fractions, which violates the requirement for \( A, B, C \) to be integers. 3. **A is not positive**: Although \( A \) is positive in the incorrect answer, the presence of fractions makes it invalid for standard form. In conclusion, the correct standard form of the equation is: \[ 2x + 7y = -11 \]