1. Patterns in a Table of Values
Chapter 6.6

2. Patterns in a Table of Values
Expression: Ex 2b + 1 or 8 – 5g or -10x + 9 Variable: Ex. 3a – 5
a combination of letters and numbers and operations (+, -, x, ÷)
a letter that represents an unknown amount
the variable is the a

3. Example 1 +2 Linear +4 +1 Straight line No common pattern Graph
Table 1 x 2 4 6 8 y 3 7 11 15
b) What is the pattern for each variable?
Table 1
x =
y =
Table 2
m =
N = +2
Linear +4
Table 2 m 1 2 3 4 N 7 8 +1
Graph
Straight line
No common pattern
Not linear
a) Graph the table of values y 16 14 12 10 8 6 4 2
c) Which relations is linear?
Graph 1 is linear.
Graph 2 is not. N 8 7 6 5 4 3 2 1 x m
Graph of Table 1
Graph of Table 2

4. Example 2 What is the difference in value in consecutive
Find the expression for the following chart
What is the difference in value in consecutive
a-values
B-Values
If linear, describe the relationship between a and B +1 +3 a B 1 3 2 6 9 4 12 +3 +1
Multiple by 3
x 3
c) What is the expression for B in terms of a
a x 3
or 3a

5. Example 3 What is the difference in value in consecutive
Find the expression for the following chart x 1 2 3 4 5 6 7 y 10 15 20 25 30 35
What is the difference in value in consecutive
x-values
y-values
If linear, describe the relationship between x and y
What is the expression for y in terms of x
5 • x
“•” means multiply
Or 5x +1 +5
Multiply by 5

6. Example 4
Photo world charges $3 for the first enlargement and $2 for each additional enlargement. What is the cost of 15 enlargements?
Make a Table of Values
b) Is this a linear relation?
# of photos n 1 2 3 4
Cost C 5 7 9
Yes
n = +1
C = +2
c) Write the expression for the cost in relation to the number of enlargements? 2n
check?  not true
2n + 1
d) What is the cost of 15 enlargements?
C = 2n + 1
C = 2(15) + 1
C = 31
Cost of 15 photos would be $31.

7. Example 5 - Sara sells magazine subscriptions
Example 5 - Sara sells magazine subscriptions. She receives $20 for every five subscription she sells. How much does she get for selling 40 subscriptions?
# of subscriptions 5 10 15 20 25 30 35
Pay $ 40 60 80
100
120
140 s P
Table of Values
Is this a linear relation?
+5 & therefore – Yes
c) What is the expression of her pay in relation to the number of subscriptions she sells?
Slope = = 4
Expression = 4s
check?  true
d) How much does she get for selling 40 subscriptions?
P = 4s
P = 4(40)
P = 160
Sara gets paid $160.

8. Example 6 Is it linear? b) What is the expression for y in terms of x?
Find the expression for the following chart
Is it linear?
x-values
y-values
b) What is the expression for y in terms of x?
Slope = = 2 2x
check?  not true yet…..
2x -1
Table 1 x 2 4 6 8 y 3 7 11 15 +2
Yes +4

9. 9.2 Patterns in a Table of Values – Practice Apply #7-11