How do I find an equation to a line parallel to the line whose equation is 3y=2x +3?

Question

I need help how to do it step by step.

Answer 1

3y=2x +3

y = 2x/3 + 3/3

y = 2x/3 + 1 ⇒  slope = 2/3, coeficient = 1

an equation to a line parallel to the line, will have same slope and different coeficient

y = 2x/3 + 2 or

y = 2x/3 - 2 or

y = 2x/3 - 5 or

Answer 2

3y = 2x + 3  Solve for y first.  This will give you slope intercept format.

y = 2/3x + 3/3 or 1

a line parallel to this is any line that has a different y-intercept.

M = slope = 2/3

b = y-intercept = 1

So, a parallel line can be

y = 2/3x - 1    or

y = 2/3x + 10002