Question

write a rule for the linear function (-4)(16),(0)(0),(4)(-16),(8)(-32)

Answer 1

The linear rule should look like this y=a*x+b
As the function graph goes through the (0,0) point, the equation 0=a*0+b <=> b=0 must be true.
Now we only need to find a, using one of the points given. With (-4, 16):
16=-4*a <=> a=16/-4 <=> a= -4
So the rule looks the following way:
f(x)= -4*x 

Answer 2

y=-4x
where x is the first value and y the second value in each pair.