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The given equation is:

\[
y = \frac{2}{3}x - 6
\]

We need to find which of the equations (A, B, C, or D) is equivalent to this in the form \(Ax + By = C\).

### Step 1: Convert the equation to standard form.
The equation is currently in slope-intercept form (\(y = mx + b\)). To convert it to standard form \(Ax + By = C\), follow these steps:

\[
y = \frac{2}{3}x - 6
\]

First, eliminate the fraction by multiplying both sides of the equation by 3:

\[
3y = 2x - 18
\]

Next, move the \(2x\) term to the left side:

\[
-2x + 3y = -18
\]

We can multiply the whole equation by \(-1\) to get rid of the negative sign:

\[
2x - 3y = 18
\]

### Step 2: Compare the result with the given options.
We see that the equation \(2x - 3y = 18\) matches option D.

### Final Answer:
The correct answer is **D**.

Would you like more details on any step, or do you have any further questions?

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Here are 5 related questions for you:
1. How do you convert an equation from slope-intercept form to standard form?
2. What are the steps to eliminate fractions in an equation?
3. How can you find the slope of a line from a standard form equation?
4. What is the difference between slope-intercept form and standard form?
5. How do you graph a line from an equation in standard form?

**Tip:** When converting between forms of an equation, always keep the coefficient of \(x\) positive in the standard form.

Which equation is equivalent to y = (2/3)x - 6?

Learn how to convert the linear equation y = (2/3)x - 6 to standard form Ax + By = C. Step-by-step solution provided. Suitable for students in Grades 8-10.

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