How would i even answer i know i learned a little but i'm having domain troubles

First transform the line into slope-intercept form (like the hint states)

8x-4y+15=0
8x+15=4y
2x+(15/4)=y
y=2x+(15/4)
so m of the given line is 2 and b=15/4

for two lines with m1 and m2, they are perpendicular if m1*m2=-1
-> insert the known m into m1:
2*m2=-1
m2=-1/2

so your new line is y=(-1/2)x+b

insert the point (3,4) it passes

4=(-1/2)*3+b
4=(-3/2)+b
11/2=b

y=(-1/2x)+(11/2)