Question

Which equations are equivalent to Y=2/3X-4 when written in slope-intercept form? Check all that apply. A =3X-2Y=4. B=2X-3Y=12. C-4(2X-3Y)=-4(12). D=2(X+6)=3Y. E=2X-3Y=4

Answer 1

The slope-intercept form: y = mx + b.

The standard form: Ax + By = C.

We have:

`y=(2)/(3)x-4` multiply both sides by 3

`3y=2x-12` subtract 2x from both sides

`-2x+3y=-12` change the signs

`2x-3y=12\to\boxed{B.}` multiply both sides by (-4)

`-4(2x-3y)=-4(12)\to\boxed{C.}`

Answer: B and C.

A. 3x - 2y = 4 - NOT

D. 2(x + 6) = 3y → 2x + 12 = 3y → 2x - 3y = -12 - NOT

E. 2x - 3y = 4 - NOT

Answer 2

B 2X-3Y=12

C -4(2X-3Y)=-4(12)

Explanation:

y = 2/3 x -4

multiply by 3

3y = 2x -12 factor out a 2 3y = 2(x-6)

subtract 2x from each side

-2x+3y = -12

multiply by -1

2x-3y = 12

multiply by -4

-4(2x-3y) = -4(12)