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:

$y=\frac{2}{3}x-6$

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:

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

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

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

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.