Question

Tomas wrote the equation y = 3x +3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas’s equation. Which equation could be Sandra’s?
–6x + y = 3/2
6x + y = 3/2
–6x + 2y = 3/2
6x + 2y = 3/2

Answer 1

In order for Sandra's equation to have all the same solutions as Tomas's equation they need to lie on each other or in other words to be exactly the same.

So now we need to transform options in tomas equation form and compare.

First option:
y = 6x + 3/2    not the same

Second option:
y = -6x + 3/2   not the same

Third option:
-6x + 2y = 3/2   when -6x goes on other side it changes its sign and will become:
2y = 6x + 3/2
when we divide by 2 we get
y = 3x + 3/4 which marks with Tomas's equation

Answer is third option.

Answer 2

–6x + 2y = 3/2

or, 2y= 6x + 3/2
or, y= (6x + 3/2)/2
or, y = 6x/2 + 3/4
or, y = 3x + 3/4

Therefore, –6x + 2y = 3/2 is Sandra's equation.