Question

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

Answer 1

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

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

First, we need to find the change in y and the change in x.

Change in y = 8 - 4 = 4
Change in x = -3 - 1 = -4

Now, we can calculate the rate of change:

Rate of change = 4 / -4
Rate of change = -1

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

To find the initial value, we can use the formula for a linear function, y = mx + b, where m is the rate of change and b is the initial value.

Using the first point on the table (1, 4), we can substitute the values in the formula:

4 = -1 * 1 + b
4 = -1 + b
b = 4 + 1
b = 5

Therefore, the initial value of the linear function given in the table is 5.