Use the table to answer the 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.
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.