Find the equation of the line parallel to the line 3x + 2y = 8 and passing through the point (0, 1).

Given,

⇒ 3x + 2y = 8

⇒ 2y = -3x + 8

⇒ y = $-\dfrac{3}{2}x + \dfrac{8}{2}$

Comparing above equations with y = mx + c we get,

Slope = $-\dfrac{3}{2}$

Since, parallel lines have equal slope.

∴ Slope of line parallel to 3x + 2y = 8 is $-\dfrac{3}{2}$.

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 1 = $-\dfrac{3}{2}(x - 0)$

⇒ 2(y - 1) = -3x

⇒ 2y - 2 = -3x

⇒ 3x + 2y - 2 = 0.

Hence, equation of the line passing through (-2, 1) and parallel to 3x + 2y = 8 is 3x + 2y - 2 = 0.