This document discusses linear function tables, which represent data with two columns - one for x-values and one for corresponding y-values. It provides examples of writing sequences as tables and finding the slope (rate of change) from tables. It also explains how to write a sequence given a table by either using existing x-values and their y-values or extending the table using the slope to find missing x-values.

1. 1.2 Linear Function Tables

2. What are Function Tables?
• A table is another way to represent data.
• Similar to a sequence, it has numbers in
order.
• But, our tables will have two parts:
▫ One for x values
▫ And one for y values
• Examples:
x 0 1 2 3
y 4 7 10 13
x y
0 4
1 7
2 10
3 13

3. Writing a Sequence in a Table
• Terms of the sequence are the y values.
• Number the terms, starting with 0.
▫ These are the x values
• Example 1:
4, 10, 16, 22, …
x
y

4. Example 2
•Write the sequence in a table.
14, 11, 8, 5, …
x y

5. You Try!
•Write the sequence in a table.
52, 45, 38, 31, …
x y

6. Finding Slope from a Table
• Rate of Change (slope) =
• Example 1:
• x 0 1 2 3 Slope = _____
y -5 -1 3 7

7. Example 2
• Find the slope/rate of change:
x y Slope = _____
0 1
5 3
10 5
15 7

8. You Try!
• Find the slope/rate of change:
x 2 4 6 8
y 24 20 16 12

9. Writing a Sequence from a Table
• Need to find terms numbered
0, 1, 2, and 3
• If 0, 1, 2, and 3 are already x values in
the table:
▫Write their corresponding y values in order
to make a sequence.

10. • If 0, 1, 2, and 3 are not x values in the
table:
▫ Use the slope to find them.

11. Example 1
•Write the first 4 terms of a sequence from
the table:
x -2 -1 0 1 2 3 4
y 8 6 4 2 0 -2 -4
• Sequence:

12. You Try!
•Write the first 4 terms of a sequence from
the table:
x -1 0 1 2 3 4
y -1 3 7 11 15 19
• Sequence:

13. Example 2
•Write the first 4 terms of a sequence from
the table:
x -6 -4 -2 0 2 4 6
y 24 18 12 6 0 -6 -12
• (Find the slope and use it to determine
the missing points you need.)

14. You Try!
•Write the first 4 terms of a sequence from
the table:
x -9 -6 -3 0 3 6
y -4 8 20 32 44 56

15. Example 3
• What if 0, 1, 2, and 3 are all missing from
the table?
• Use the slope to extend the table and find
them!
• Let’s write a sequence from:
x 5 10 15 20 25
y 70 60 50 40 30

16. You Try!
•Write a sequence from:
x -10 -8 -6 -4 -2
y 17 19 21 23 25