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

Given,

⇒ 3x + 2y = 8

Converting 3x + 2y = 8 in the form y = mx + c we get,

⇒ 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)

Thus, equation of line with slope $-\dfrac{3}{2}$ and passing through (0, 1) is :

⇒ y - 1 = $-\dfrac{3}{2}$(x - 0)

⇒ 2(y - 1) = -3x

⇒ 2y - 2 = -3x

⇒ 3x + 2y = 2 .

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