Me.
show all work: from the line y-2x-10 find the equation of the line that is perpendicular to this line and goes through the point (9,-5)

Not sure if y-2x=10 or y-2x=-10

I'll solve both
later you will see that 10 or -10 is irrelevant

find slope first since perpendicular lines have slopes that multiply to -1
the slope from form ax+by=c is -a/b
-2x+y=?
slope=-(-2)/1=2

perpendicualr
2 times what=-1
what=-1/2

y=mx+b
m=slope
we know slope is -1/2
y=-1/2x+b
find b
subsitut eht point (9,-5)
(x,y)
x=9 and y=-5
-5=-1/2(9)+b
-5=-9/2+b
add 9/2 to both sides
-1/2=b

the equation is
y=-1/2x-1/2