We have to find the equation that is equivalent to:
[tex]y=\frac{1}{3}x-2[/tex]
We can manipulate the equation in order to find if the other equations are equivalent.
(A) The term 1/3*x would be negative on the left side of the equation, so this is not equivalent.
We can multiply both sides by 3 and get:
[tex]3y=x-6[/tex]
(B) is not equivalent, because the relation between the coefficients of x and y is different (they will have different slope).
(C) the coefficients are right, but not the independent term (it should be -6, not -2).
(D) this expression is equivalent:
[tex]\begin{gathered} y=\frac{1}{3}x-2 \\ y\cdot3=\frac{1}{3}x\cdot3-2\cdot3 \\ 3y=x-6 \\ -x+3y=-6 \end{gathered}[/tex]
Answer: Option D.
