Question

Find the value of $$k$$ for which the lines $$kx + 2y + 3 = 0$$ and $$8x + ky - 1 = 0$$ are parallel.

Answer 1

Convert each line into the slope-intercept form $$y = mx + c$$:

For $$kx + 2y + 3 = 0$$:

$$2y = -kx - 3$$

$$y = -\frac{k}{2}x - \frac{3}{2}$$

Slope $$m_1 = -\frac{k}{2}$$

For $$8x + ky - 1 = 0$$:

$$ky = -8x + 1$$

$$y = -\frac{8}{k}x + \frac{1}{k}$$

Slope $$m_2 = -\frac{8}{k}$$

For parallel lines, $$m_1 = m_2$$:

$$-\frac{k}{2} = -\frac{8}{k}$$ 

$$k^2 = 16$$

$$k = \pm 4$$