Question

If the lines $$2x - by + 5 = 0$$ and $$ax + 3y = 2$$ are parallel, find the relation connecting $$a$$ and $$b$$.

Answer 1

Find the slopes of both lines:

For $$2x - by + 5 = 0$$: 

$$by = 2x + 5$$

$$y = \frac{2}{b}x + \frac{5}{b}$$ 

Slope $$m_1 = \frac{2}{b}$$

For $$ax + 3y = 2$$: 

$$3y = -ax + 2$$ 

$$y = -\frac{a}{3}x + \frac{2}{3}$$ 

Slope $$m_2 = -\frac{a}{3}$$

Since the lines are parallel, their slopes are equal:

$$m_1 = m_2$$

$$\frac{2}{b} = -\frac{a}{3}$$ 

$$ab = -6$$ or $$ab + 6 = 0$$