First you want to find the slope of the reference line. We are given a line in standard form ax+by=c, and we can rearrange this into point slope form, y=mx+b where m=slope.
2x+3y=-5 subtract 2x from both sides
3y=-2x-5
y=(-2x-5)/3
So the slope of the reference line is -2/3
For lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically:
m1*m2=-1 ie: the product of the slopes is negative one.
In this case our perpendicular line must have a slope of:
m(-2/3)=-1
-2m=-3
m=3/2
m=1.5
So far we now have:
y=1.5x+b, using the point (-6,1) we can solve for b, the y-intercept...
1=1.5(-6)+b
1=-9+b
10=b
So the perpendicular line is:
y=1.5x+10