30 POINTS!! WILL VOTE BRAINIEST

The table shows a linear function

(a) Determine the difference of outputs of any two inputs that are 1 unit apart. Show your work.
(b) Determine the difference of outputs of any two inputs that are 2 units apart. Show your work.
(c) Determine the difference of outputs of any two inputs that are 3 units apart. Show your work.
(d) What do you notice about the ratios of the differences in the outputs to the input intervals? Explain your answer.

Part A:

Consider from x = -5 to x = -4, they are 1 unit apart and the difference of their outputs is given by:

-3 - (-11) = -3 + 11 = 8.

Thus, the value of the output increases by 8 units for each one unit increase in the input.

Part B:

Consider from x = -3 to x = -1, they are 2 units apart and the difference of their outputs is given by:

21 - 5 = 16.

Thus, the value of the output increases by 16 units for each two units increase in the input.

Part C:

Consider from x = 0 to x = 3, they are 3 units apart and the difference of their outputs is given by:

53 - 29 = 24.

Thus, the value of the output increases by 24 units for each three units increase in the input.

Part D:

It can be noticed that the ratio difference in the outputs to the input intervals are equal for all the given input intervals.

i.e 8 / 1 = 16 / 2 = 24 / 3.