Write in standard form: \[ \begin{array}{l}y=\frac{2}{3} x-6 \\ \text { A. } 3 y=2 x-18 \\ \text { B. } 2 x-3 y=18 \\ \text { C. } 3 y=2 x-6 \\ \text { D. } 2 x-3 y=6 \\ \text { E. }-2 x+3 y=6\end{array} \] \[ \]

To convert the equation \( y = \frac{2}{3}x - 6 \) into **standard form**, we follow these steps: **Standard Form of a Linear Equation:** \[ Ax + By = C \] where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative. **Steps to Convert:** 1. **Start with the given equation:** \[ y = \frac{2}{3}x - 6 \] 2. **Eliminate the fraction by multiplying every term by 3:** \[ 3y = 2x - 18 \] 3. **Rearrange the equation to get all variable terms on one side and constants on the other:** \[ 2x - 3y = 18 \] **Final Standard Form:** \[ 2x - 3y = 18 \] **Matching with the Given Options:** - **A.** \( 3y = 2x - 18 \) - **B.** \( 2x - 3y = 18 \) - **C.** \( 3y = 2x - 6 \) - **D.** \( 2x - 3y = 6 \) - **E.** \( -2x + 3y = 6 \) **Correct Answer:** **B. \( 2x - 3y = 18 \)**