Hey there!
First let's look at our equations.
Y= -1/4x+9 This looks like it can go in a graphing calculator just as it is.
32x-8y=-8 For this equation, we have to determine the value of Y.
32x-8y=-8
-32x-8y= -8-32x
-8y=-32x-8
+8 +8
y=-32x
Now put these equations in a calculator, and you'll see these lines are Perpendicular.
I hope this helps!