Since the line in question is parallel to the line with the equation 3x+2y-6=0, it can be said that they have the same slope. To find the slope of the line with the given equation, transform the given equation to its corresponding slope-intercept form. Hence, the equation is now
y=(-3/2)x+3
the slope is then -3/2
and since the line in question passes through the origin, the equation of this line is then
y=(-3/2)x+0
or simply
y=(-3/2)x
