Question 26593
Here's what I would do:
First, I would find the slope (which you did right)
The slope is {{{2/3}}}
The work you did found the line that went through (-4,8), but wasn't perpendicular to {{{2x-3y=1}}}. That was your mistake.
To find a perpendicular line, the slope will be the negative reciprocal.
So, the slope of your line will be {{{-3/2}}}.
To find the y-intercept, the easiest way is to plug the coordinates you already have back into slope-intercept form, which is {{{y=mx+b}}}.
{{{8=(-3/2)*-4+b}}}
*[invoke explain_simplification "8=(-3/2)*-4+b"]
So, you find that your y-intercept is 2.
The final formula in function notaion would be {{{f(x)=-(3/2)x+2}}}
To check, graphing it may be helpful.
{{{graph(500,500,-10,10,-10,10,-(3/2)x+2,(2/3)x-(1/3))}}}
The GREEN line is the original, and the RED line is the one you were trying to solve for. 
From the graph, you can indeed see that the lines are parrallel.
Hope this helps!