6question write a rule for the linear function in the table

To write a rule (equation) of linear function of we can use any two points from the table.

I am using the first and last point to solve the question. First point is (1, -7) and the last point is (4, -16).

First we find the slope(m) from these points. Slope of the line will be



Using the slope m=-3 and a point (4,-16), we can write the equation using point-slope form as:

y - (-16) = -3 (x-4)
y + 16 = -3x + 12
y = -3x + 12 - 16
y = -3x - 4

Therefore, option A gives the correct rule of the linear function shown in the table.