A rhombus is on a coordinate plane and has one of its sides modeled by the equation 3y - 4x = 35. determine which of the following equations could model the opposite side of the rhombus. Select all that apply.

A. y = 4/3 x + 16/3

B. y - 3 = 3/4 (x - 8)

C. 8x - 6y = 38

D. 9y = 12x - 27/14

E. 2x + y = - 5

F. 4x - 3y = 12

A. y = 4/3 x + 16/3.

C. 8x - 6y = 38

D. 9y = 12x - 27/4

F. 4x - 3y = 12.

Step-by-step explanation:

A rhombus has parallel opposite sides so the lines will have the same slope as:

3y - 4x = 35

We convert to slope - intercept form:

3y = 4x + 35

y = 4/3 x + 35/3

- so the slope of this line is 4/3.

Now the opposite side will also have a slope of 4/3 but a different y-intercept.

So A. y = 4/3 x + 16/3 is one of the required equations.

8x - 6y = 38

6y = 8x - 38

y = 4/3 x - 38/6. (C)

- The same slope, so this could also be one of the required equations.

9y = 12x - 27/4

y = 4/3 x - 27/36 (D)

- so this could also be one of the required equations.

4x - 3y = 12

3y = 4x - 12

y = 4/3 x - 4.

This is one also (F).

B and E have slopes of 3/4 and - 2 so could not be models for the opposite side.