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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UpStudy AI · Accepted Answer

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. $$ 2x - 3y = 18 $$**
The standard form of the equation $$ y = \frac{2}{3}x - 6 $$ is $$ 2x - 3y = 18 $$.

Write in standard form:

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