JAMB 2002 · UME · Q8

Find the value of $k$ if the line $2y - kx + 4 = 0$ is perpendicular to the line $y + \frac14x - 7 = 0$ .

Worked solution (try it first)

Rearrange $2y - kx + 4 = 0$ : $2y = kx - 4$ , so $y = \frac k2x - 2$ and the gradient is $\frac k2$ .
Rearrange $y + \frac14x - 7 = 0$ : $y = -\frac14x + 7$ , so the gradient is $-\frac14$ .
Perpendicular gradients multiply to $-1$ : $\frac k2 \times \left(-\frac14\right) = -1$ , so $\frac k8 = 1$ .
So $k = 8$ , option D.