Question 92090
L has y-intercept (0,2) and is perpendicular to the line with equation 
2x-3y=6.
In order to find the equation of a line we need a slope.  Perpendicular lines have slopes that are negative reciprocals of each other.  That means that they are opposite signs and upside down from each other.
The slope-intercept form of a line is: {{{highlight(y=mx+b)}}}, where m=slope and (0,b)=y-intercept.
Put 2x-3y=6 into slope-intercept form by solving for y:
{{{2x-3y=6}}}
{{{-2x+2x-3y=-2x+6}}}
{{{-3y=-2x+6}}}
{{{-3y/-3=(-2/(-3))x+6/(-3)}}}
{{{y=(2/3)x-2}}}
The slope of this line is m=2/3, so the slope of your line is m=-3/2
Now plug m=-3/2 and (0,b)=(0,2) into the slope intercept form:
{{{highlight(y=(-3/2)x+2)}}}
Happy Calculating!!!