Given that (3x + 4y + 6 = 0) and (4x – by + 3 = 0) are perpendicular, find the value of b.
-
A.
4 -
B.
3 -
C.
(frac{1}{3}) -
D.
(frac{1}{4})
Correct Answer: Option B
Explanation
When you have two lines, (y_{1}, y_{2}), perpendicular to each other, the product of their slopes = -1.
(3x + 4y + 6 = 0 implies 4y = -6 – 3x)
(therefore y = frac{-6}{4} – frac{3}{4}x)
(frac{mathrm d y}{mathrm d x} = frac{-3}{4})
Also, (4x – by + 3 = 0 implies by = 4x + 3)
(y = frac{4}{b}x + frac{3}{b})
(frac{mathrm d y}{mathrm d x} = frac{4}{b})
(frac{-3}{4} times frac{4}{b} = -1 implies frac{4}{b} = frac{4}{3})
(b = 3)