What is the standard form of the linear equation y - 4 = (2/3)(x + 9)?

To determine the standard form of the linear equation given as y - 4 = (2/3)(x + 9), we start by simplifying and rearranging the equation step by step.

First, distribute the (2/3) on the right side:

y - 4 = (2/3)x + (2/3)(9)

Calculate (2/3)(9), which simplifies to 6. Thus, the equation becomes:

y - 4 = (2/3)x + 6

Next, isolate y on one side by adding 4 to both sides:

y = (2/3)x + 10

Now, to convert this equation into standard form (Ax + By = C), where A, B, and C are integers, we need to eliminate the fraction. We can do this by multiplying every term by 3 (the denominator):

3y = 2x + 30

Rearranging this equation to bring all terms to one side gives:

2x - 3y = -30

This is now in standard form, complying with the requirements that A is positive and all terms are arranged correctly.

The correct answer matches the derived equation precisely, confirming it is the proper standard