what rule matches the function represented by the table?

Let's try a line
y = mx + b
From (0,4):
4 = 0x + b
b = 4
So far we have
y = mx + 4
From (1,1)
1 = m(1) + 4
-3 = m
Our rule is y = -3 x + 4
Let's check the other points:
-3(-4)+4 = 12+4 = 16 good
-3(4)+4 = -12+4 = -8 good
-3(9) + 4 = -23 good
Answer: y = -3 x + 4