Question 26862
Same as the other type of problem, only this time you need to use the fact that <i>perpendicular to</i> means the same as "has a slope that is the negative reciprocal of" Finding the slope now requires rearranging the line the give you:
{{{2x-3y=6}}}
{{{-3y=-2x+6}}}
{{{y=2/3x-2}}}
Now you have your slope (m from the equation y=mx+b) as 2/3. But for your line, you want something that is perpendicular, or has a negative reciprocal slope. To find the negative reciprocal of a number, you take -1 and divide it by the number.

{{{(-1)/(2/3)=-3/2}}}
So -3/2 will be the slope for your line, and again they give you a y-intercept (2). So putting that into slope-intercept format gives:
{{{y=-3x/2+2}}}