Question

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

Answer 1

slope of 4x-y=1......4
of 5x-ky=2.....5/k

since lines are perp. ,4×(5/k) =-1

Answer 2

Answer:  $k=-20$

Step-by-step explanation:

We know that the Slope of line $y=mx+c$ is m.

Rewrite $4x-y=1$ in the standard form, we get $y=4x-1$

Thus, the slope of line  $4x-y=1$ =4

Similarly,$5x-ky=1\\\Rightarrow\ y=\frac{5}{k}-\frac{1}{k}$

the slope of line $5x-ky=1$= $\frac{5}{k}$

We know that if two lines are perpendicular then the product of two lines equals to -1.

Thus, $4\times\frac{5}{k}=-1\\\Rightarrow\ k=-20$