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 correct options are b and c.

Explanation:

The given equation is

`y=(2)/(3)x-4`

The slope intercept form of a linear equation is

`y=mx+b`

In option a,

`3x-2y=4`

`3x-4=2y`

Divide both sides by 2.

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

Therefore option a is incorrect.

Similarly rewrite all equations in their slope intercept form.

In option b,

`2x-3y=12`

`2x-12=3y`

`(2)/(3)x-4=y`

Therefore option b is correct.

In option c,

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

`2x-3y=12`

`2x-12=3y`

`(2)/(3)x-4=y`

Therefore option c is correct.

In option d,

`2(x+6)=3y`

`2x+12=3y`

`(2)/(3)x+4=y`

Therefore option d is incorrect.

In option e,

`2x-3y=4`

`2x-4=3y`

`(2)/(3)x-(4)/(3)=y`

Therefore option e is incorrect.