The given equation is
3x – 4y – 16 = 0
⇒ y = \(\frac{3}{4}\) x – 4
∴ Slope of the line, m1 = \(\frac{3}{4}\)
∴ Slope of the perpendicular line, m2 = – \(\frac{4}{3}\) .
Since the line passes through (– 1, 3), so the equation of the line is
y – y0 = m(x – x0)
⇒ y – 3 = m2 (x+ 1)
⇒ y – 3 = –\(\frac{4}{3}\)(x + 1)
⇒ 3y – 9 = – 4x – 4
⇒ 4x + 3y – 5 = 0