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.

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.

Answer Details

When two lines are parallel, their slopes are equal. In other words, the coefficient of x in one equation divided by the coefficient of y should be equal to the coefficient of x in the other equation divided by the coefficient of y. Therefore, we can write: k/(-5) = m/n Multiplying both sides by -5n, we get: kn = -5m This is the relationship connecting the constants m, n, and k. Therefore, the correct option is (2) kn + 5m = 0.