Question

hich equations are equivalent to y = two-thirds x minus 4 when written in slope-intercept form? Check all that apply. 3 x minus 2 y = 4 2 x minus 3 y = 12 Negative 4 (2 x minus 3 y) = negative 4 (12) 2 (x + 6) = 3 y 2 x minus 3 y = 4

Answer 1

Answer:

Explanation:

Given

Required

Equivalents of the given equation;

We start by multiply both sides of the equation by 3

---- Equation 1

Subtract 3y from both sides

Add 12 to both sides

Rearrange:

---- This is equivalent to the given equation;

Multiply both sides of the above equation by -4

---- This is also equivalent to the given equation;

From the list of given options, only these two are equivalent to

Explanation:

Answer 2

`2x - 3y = 12`

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

Explanation:

Given

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

Required

Equivalents of the given equation;

We start by multiply both sides of the equation by 3

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

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

`3y = 2x - 12` ---- Equation 1

Subtract 3y from both sides

`-3y + 3y = 2x - 12 - 3y`

`0 = 2x - 12 - 3y`

Add 12 to both sides

`12 + 0 = 2x - 12 - 3y + 12`

`12 = 2x - 3y`

Rearrange:

`2x - 3y = 12` ---- This is equivalent to the given equation;

Multiply both sides of the above equation by -4

`2x - 3y = 12`

`-4(2x - 3y) = -4(12)` ---- This is also equivalent to the given equation;

From the list of given options, only these two are equivalent to
`y = (2)/(3)x - 4`