To write a rule or an equation for the linear function shown in table we can use any two points.
I am using the first two points (1, -7) and (2,-10)
First we need to find the slope(m), using these points.

Using the slope and point (1,-7) we can write the equation in point slope form as:
y + 7=-3(x-1)
y = -3x + 3 - 7
y = -3x - 4
So first option gives the correct answer