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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

1 Which Of The Following Equations Are Equivalent To Y 13x2 A Y 13x 2 B 3y 3x 6 C X 3y 2 D X 3y 6 class=

Sagot :

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.

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