Question

What is the equation of the line that passes through (–2, 3) and is parallel to 2x + 3y = 6?

Answer 1

Here, Equation: 2x + 3y = 6
3y = -2x + 6

Divide both sides by 3, 
y = -2/3x + 2

Here, Slope = -2/3 and it would be same for that line which is parallel to it.
So, y - 3 = -2/3 (x + 2)
y - 3 = -2x/3 - 4/3
y = -2x/3 + 5/3

In short, Your Answer would be Option B

Hope this helps!