Question

Find the equation of a line passing through the origin and parallel to the line $$3x - 2y + 4 = 0$$.

Answer 1

The given line is $$3x - 2y + 4 = 0$$: 

$$2y = 3x + 4$$

$$\implies y = \frac{3}{2}x + 2$$ 

Slope $$m = \frac{3}{2}$$.

The parallel line has the same slope $$m = \frac{3}{2}$$. 

Passing through origin $$(0, 0)$$: 

$$y - 0 = \frac{3}{2}(x - 0)$$

$$2y = 3x$$

$$3x - 2y = 0$$