What is the equation of the line described below written in slope intercept form? the line passing through point (0,0) and parellel to the line whose equation is 3x+2y-6=0

Solve 3x+2y-6=0 for y

2y-6=-3x

2y=-3x+6

y=-1.5x+3

So the slope of the reference line is -1.5.  For two lines to be parallel they must have the same slope so our line will also have a slope of -1.5 so we have:

y=-1.5x+b, now we can solve for b given the point (0,0)

0=-1.5(0)+b

0=0+b

b=0 so our line is:

y=-1.5x