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:

$y=\dfrac{2}{3}x-4$       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

Answer:

B  2X-3Y=12

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

Step-by-step 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)