So, basically you'll need to change the equation 8x-5y=3 into y=mx+b format.
If you do that, you'll get
y=8/5x - 3/5
Now, you know the slope of the equation. It's positive 8/5.
Using the equation of a line y-y1=m(x-x1), plug in the values of the coordinate 8x-5y=3 passes through.
So... you'll get:
y-(-1)=8/5(x-(-2))
y+1=8/5(x+2)
From here on, just simplify so you can get the slope intercept form.
y = 8/5x + 11/5
However, you're not done yet. The problem is looking for an equation of a line perpendicular to the one we currently have. So, we need the slope which is perpendicular to 8/5.
In order to get that, we need to use the negative reciprocal. So, basically we switch the places of the numerator and denominator and make it a negative.
The perpendicular reciprocal of 8/5 is -5/8.
Looking at the choices above, the only choice given with -5/8 as the slope is A.
So, the answer is: A y = -5/8x - 9/4