Question

Which equation is equivalent to y = (2/3)x -6? 1. 2x + 3y = -62. 3x - 2y = -63. 3x - 2y = 124. 2x - 3y = 18

Answer 1

Given the equation:

`y=(2)/(3)x-6`

You can follow these steps in order to find an equivalent equation:

1. Apply the Addition Property of Equality by adding 6 to both sides of the equation:

`\begin{gathered} y+(6)=(2)/(3)x-6+(6) \\ \\ y+6=(2)/(3)x \end{gathered}`

2. Apply the Multiplication Property of Equality by multiplying both sides of the equation by 3:

`\begin{gathered} 3(y+6)=((2)/(3)x)(3) \\ \\ (3)(y)+(3)(6)=2x \\ \\ 3y+18=2x \end{gathered}`

3. Apply the Subtraction Property of Equality by subtracting this term from both sides of the equation:

`3y`

Then:

`\begin{gathered} 3y+18-(3y)=2x-(3y) \\ \\ 18=2x-3y \end{gathered}`

4. Rewrite the equation in this form:

`2x-3y=18`

Therefore, the answer is: Option 4.