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

Converting 3x - 2y + 4 = 0 in the form y = mx + c we get,

⇒ -2y = -3x - 4

⇒ y = $\dfrac{-3x}{-2} - \dfrac{4}{-2}$

⇒ y = $\dfrac{3x}{2}$ + 2

Comparing above equation with y = mx + c we get, m = $\dfrac{3}{2}$

Since the required line is parallel to the given line, they must have the same gradient:

⇒ Slope of parallel line = $\dfrac{3}{2}$

Using the slope-intercept form y = mx + c. Since the line passes through the origin, the y-intercept is 0.

⇒ y = $\dfrac{3}{2}$x + 0

⇒ 2y = 3x

⇒ 3x - 2y = 0.

Hence, the equation of the required line is 3x - 2y = 0.