We have given an equation of line 3x – 4y + 2 = 0 ... (i)
Slope of the line (i) =

3

4

Thus, slope of any line parallel to the given line (i) is

3

4

and passes through (–2, 3), then its equation is
y - 3 =

3

4

(x (- 2)) ⇒ 4y - 12 = 3x + 6
⇒ –4y + 12 + 3x + 6 = 0 ⇒ 3x – 4y + 18 = 0