8x + 5y = 2 → 5y = - 8x + 2 → y = (-8/5)x + 2 ⇒ m = -8/5
perpendicular slope = 5/8
Point-Slope formula: y - y₁ = m(x - x₁) ; where (x₁, y₁) is the given point
y - (-7) = (5/8)(x - 2)
y + 7 = (5/8)(x - 2)
8(y + 7) = 5(x - 2)
8y + 56 = 5x - 10
8y + 66 = 5x
66 = 5x - 8y ⇒ 5x - 8y = 66
Answer: 5x - 8y = 66