Question

1. Which of the following equations are equivalent to y = 1/3*x-2 (A) y + 1/3*x = -2 (B) 3y = 3x - 6 (C) -x + 3y = -2 (D) -x + 3y = -6

Answer 1

We have to find the equation that is equivalent to:

`y=(1)/(3)x-2`

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:

`3y=x-6`

(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:

`\begin{gathered} y=(1)/(3)x-2 \\ y\cdot3=(1)/(3)x\cdot3-2\cdot3 \\ 3y=x-6 \\ -x+3y=-6 \end{gathered}`

Answer: Option D.