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.
(1 point)

The rate of change is m = __, and the initial value is b = __.

Answer 1

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

m = (change in Y) / (change in X)

In this case, the change in Y is 8 - 4 = 4, and the change in X is -3 - 1 = -4.

So, the rate of change is:

m = 4 / -4 = -1

To find the initial value (y-intercept), we can substitute one of the points into the equation y = mx + b and solve for b.

Using the point (1, 4):

4 = -1(1) + b
4 = -1 + b
b = 5

So, the initial value is:

b = 5

Therefore, the rate of change is m = -1, and the initial value is b = 5.