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 = (3)/(2)x-4.`

We can now easily identify the slope:

`m = (3)/(2).`

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

`y = (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= (3)/(2)x}.`