Tables

First Difference

Example

Write the equation for the function that contains the points in the table below.

First_ex1

Step 1. Make sure the x-values have a constant change.

3 - 2 = 1

2 - 1 = 1, etc.

Yes: 1

Step 2. Find the change from one y-value to the next.

-8-(-2) = -6

-2 - 4 = -6, etc.

Step 3. Use the "first difference" to write a formula.

a = -6

y -intercept, b = (0, 10) as found in the table

Step 4. Substitute values into y = ax + b

y = -6x + 10