Recalll that the general equation fo the line is of the form y=mx+b where m is the slope and b is the y intercept. Also, remember that if we have two lines y=m1x+b1 and y=m2x+b2, they are perpendicular if and only if m1*m2=-1.
Let's construct the equation of the line we want. Say y=mx+b. So we must find the value of m and b. We are given the line y=5x-4. The slope of this line is 5. Since we want them to be perpendicular, it must happen that
if we divide by 5 on both sides, we get
this means that the equation we want, so far, is
Now, since this line passes through the point (3,8) it must happen that whenever we replace x by 3, y should be replaced by 8. Then we have the equation
Then, if we add 3/5 on both sides, we get
So, the equation of our perpendicular line is