Given that the straight lines \(kx - 5y + 6 = 0\) and \(mx + ny - 1 = 0\) are parallel, find a relationship connecting the constants m, n and k.

A.

5n - km = 0

B.

kn + 5m = 0

C.

5n + km = 0

D.

kn - 5m = 0

Correct answer is B

Two lines are parallel if and only if their slopes are equal.

\(kx - 5y + 6 = 0 \implies 5y = kx + 6\)

\(y = \frac{k}{5}x + \frac{6}{5}\)

\(Slope = \frac{k}{5}\)

\(mx + ny - 1 = 0 \implies ny = 1 - mx\)

\(y = \frac{1}{n} - \frac{m}{n}x\)

\(Slope = -\frac{m}{n}\)

\(Parallel \implies \frac{k}{5} = -\frac{m}{n}\)

\(-5m = kn \implies 5m + kn = 0\)