Use the table to answer the question.

Question

x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.

Answer 1

To find the rate of change, we can use the formula:

rate of change = (change in y) / (change in x)

From the table:
change in y = 8 - 4 = 4
change in x = -3 - 1 = -4

rate of change = 4 / -4 = -1

Therefore, the rate of change of the linear function is -1.

To find the initial value of the linear function, we can use the formula:

y = mx + b

Using the first point (1,4):
4 = -1(1) + b
4 = -1 + b
b = 5

Therefore, the initial value of the linear function is 5.