Write in standard form: \[ \begin{array}{l}y=\frac{2}{3} x-6 \\ \text { A. } 3 y=2 x-18 \\ \text { B. } 2 x-3 y=18 \\ \text { C. } 3 y=2 x-6 \\ \text { D. } 2 x-3 y=6 \\ \text { E. }-2 x+3 y=6\end{array} \] \[ \]
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To write the equation \( y = \frac{2}{3} x - 6 \) in standard form, we want to rearrange it into the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers. Starting with the given equation: \[ y = \frac{2}{3} x - 6 \] First, we can eliminate the fraction by multiplying the entire equation by 3: \[ 3y = 2x - 18 \] Now, we can rearrange this to standard form by simply moving \( 2x \) to the left side: \[ -2x + 3y = -18 \] To make \( A \) positive, multiply through by -1: \[ 2x - 3y = 18 \] Matching this with the options provided: The correct answer is \( B. \, 2x - 3y = 18 \). The other possible options include incorrect coefficients or the wrong constant on the right side.
