Find k, if the line 4x - y = 1 is perpendicular to the line 5x - ky = 2?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Given,}} \cr & 4x - y = 1 \cr & \therefore y = 4x - 1 \cr & 5x - ky = 2 \cr & \therefore y = \frac{{5x}}{k} - \frac{2}{k} \cr & y = {m_1}x + C \cr & {m_1} = \frac{5}{k} \cr} $$
If the lines are ⊥ then the product of their slope is -1
\[\begin{array}{l} {m_1} \times {m_2} = - 1\\ 4 \times \frac{5}{k} = - 1\,\,\,\,\,\,\,\,\,\,\left\{ \begin{array}{l} {m_1} = 4\\ {m_2} = \frac{5}{k} \end{array} \right.\\ \therefore k = - 20 \end{array}\]