Question

Does anyone know how to solve this?

Answer 1

We may start by putting the given equation in slope-intercept from:

$3x-2y = 8 \iff 3x - 8 = 2y \iff y = \dfrac{3}{2}x-4.$

We can now easily identify the slope:

$m = \dfrac{3}{2}.$

Since parallel lines have the same slope (as you already seem to know), any line with equation

$y = \dfrac{3}{2} + b, \quad\textrm{with } b \in \mathbb{R},$

is parallel to the given line. By choosing, for instance, $b = 0$, we get:

$\boxed{y= \dfrac{3}{2}x}.$