Correct Answer – Option 2 : 2x – 3y + 12 = 0

Concept:

Equation of a Line Parallel to a Line:

Let, ax + by + c = 0 (b ≠ 0) be the equation of the given straight line. So, the equation of a line parallel to a given line is ax + by + k = 0

​Where k is constant.

The slopes of parallel lines are equal.

Calculation:

Hare, equation of the straight line parallel to 2x – 3y = 1

Let, equation of required line be 2x – 3y + k = 0

Now, this line passing through (-3, 2)

∴2(-3) – 3(2) + k = 0

⇒ -6  – 6 + k = 0 

⇒ k = 12

∴ Equation of required line 2x – 3y + 12 = 0

Hence, option (2) is correct.