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

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

• A. 2x - 3y = -30
• B. 3x + 2y = 6
• C. x + 4y = 12
• D. 4x - 2y = 20

Answer: (A)

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

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