Linear Patterns & Relationship Review

Definitions

100

What is a Linear Pattern?

is a pattern that grows or decreases by the same amount each time.

200

What is a Constant Change?

 the amount something increases or decreases by.

300

What is a term number?

The term number tells you the 

position of a number in a pattern.

400

What is an ordered Pair?

Is a pair of numbers written in a specific order that shows the location of a point on a graph.

500

What is a Linear Relationship?

 The numbers change at a constant rate +/- . When graphed, the points form a straight line.

T(n)= start +/- change (n-1)

100

Using T(n) = start + change(n − 1)

Pattern: 5, 9, 13, 17, …

a) Write the formula using T(n) = start + change(n − 1)

T(n) = 4n + 1

200

Using T(n) = start − change(n − 1)

Pattern: 30, 26, 22, 18, …

a) Write the formula using T(n) = start − change(n − 1)

T(n) = -4n + 34

300

Using T(n) Formula

Pattern: −4, 1, 6, 11, …

a) Write the formula using T(n) = start + change(n − 1)

T(n) = 5n - 9

400

Using T(n) Formula

Pattern: 100, 92, 84, 76, …

a) Write the formula using T(n) = start − change(n − 1)

T(n) = -8n + 108

500

The rule is:
T(n) = 4n -1

a) Is 49 in this pattern? Solve for n.

4n - 1 = 49

4n = 49 - 1

4n = 48

n = 48/4

n=12

y=mx+b

100

X    Y

1    9
 2    11
 3    13
 4    15

               

What is the equation for y = mx+b

y = 2x + 7

200

X    Y

1    4
2    7
 3    10
 4    13

What is the equation in the form y = mx + b?

  y = 3x + 1

300

X    Y

 1    18
 2    15
 3    12
4    9

What is the equation in the form y = mx + b?

y = -3n + 21

400

X    Y

 1    -2
 2     3
 3       8
 4    13

What is the equation in the form y = mx + b?

y = 5n -7

500

X    Y

1    25
2    20
3    15
4    10

What is the equation in the form y = mx + b?

y = -5n +30

Tiles

100

Term 1:  ( ) ( ) ( )
Term 2:  ( ) ( ) ( ) ( ) ( )
Term 3:  ( ) ( ) ( ) ( ) ( ) ( ) ( )
Term 4:  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

a) Write the equation in the form y = mx + b
b) Create a table of values for x = 1, 2, 3, 4

X             Y

1             3

2             5              y = 2x + 1

3             7

4             9

200

Term 1:  ( ) ( )
Term 2:  ( ) ( ) ( ) ( )
Term 3:  ( ) ( ) ( ) ( ) ( ) ( )
Term 4:  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

a) Write the equation in the form y = mx + b
b) Create a table of values for x = 1, 2, 3, 4

X    Y

1    2
2    4
3    6
4    8

y = 2x

300

Term 1:  ( ) ( ) ( ) ( ) ( )
Term 2:  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
Term 3:  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
Term 4:  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

a) Write the equation in the form y = mx + b
b) Create a table of values for x = 1, 2, 3, 4

X    Y

1    5
2    8
3    11
4    14

y = 3x + 2

400

Term 1:  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
Term 2:  ( ) ( ) ( ) ( ) ( ) ( )
Term 3:  ( ) ( ) ( ) ( )
Term 4:  ( ) ( )

a) Write the equation in the form y = mx + b
b) Create a table of values for x = 1, 2, 3, 4

X   Y

1   8
2   6    y = -2x + 10
3   4
4   2

500

Term 0:  ( ) ( ) ( )
Term 1:  ( ) ( ) ( ) ( ) ( )
Term 2:  ( ) ( ) ( ) ( ) ( ) ( ) ( )
Term 3:  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

a) Write the equation in the form y = mx + b
b) Create a table of values for x = 1, 2, 3, 4

X   Y

0   3
1   5    y = 2x + 3
2   7
3   9