Conner Tyler
07/21/2024 · Junior High School

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: \( A x+B y=C \) Answer fails to make sure \( A, B, C \) are not fractions (or decimals). Answer fails to make sure \( A \) is positive.

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To convert the equation \( y = -\frac{2}{7} x - \frac{11}{7} \) into standard form \( Ax + By = C \), we need to rearrange it and eliminate any fractions. 1. Start with the given equation: \[ y = -\frac{2}{7} x - \frac{11}{7} \] 2. To eliminate the fractions, multiply every term by 7 (the denominator): \[ 7y = 7 \left(-\frac{2}{7} x\right) + 7 \left(-\frac{11}{7}\right) \] This simplifies to: \[ 7y = -2x - 11 \] 3. Rearrange the equation to get it into standard form \( Ax + By = C \): \[ 2x + 7y = -11 \] 4. In standard form, we want \( A \) to be positive. Since \( A = 2 \) is already positive, we do not need to change the signs. Thus, the final standard form of the equation is: \[ 2x + 7y = -11 \] ### Summary of the Incorrect Answer: The incorrect answer \( \frac{2}{7} x + y = -\frac{11}{7} \) fails to meet the standard form criteria because: - It contains fractions, which is not allowed in standard form. - The coefficient \( A \) (which is \( \frac{2}{7} \)) is not an integer. - The equation is not arranged in the correct format \( Ax + By = C \) with \( A \) being positive. The correct standard form is \( 2x + 7y = -11 \).

Quick Answer

The correct standard form is \( 2x + 7y = -11 \). The incorrect answer contains fractions and does not follow the standard form format.
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