Algebra 1 Common Core Student Edition, Grade 8-9

Step 1

W hich v a r ia b le is th e
dependent variable?
The perimeter depends
on the number of
rectangles, so perimeter
is the dependent variable.

M a k e a t a b le. U s e x as th e

in d e p e n d e n t va ria b le a n d y

as th e d e p e n d e n t v a ria b le.

Let x = the num ber o f rectangles.

Let y = the p e rim e te r o f the figure.

W r it e e a c h p a i r o f i n p u t a n d o u t p u t

values x a n d y as a n o r d e r e d p a ir

(x,y)-

1

2

3

4

2(1) + 2(6) = 14

2(2) + 2(6) = 16

2(3) + 2(6) = 18

2(4) + 2(6) = 20

(1, 14)

( 2 , 16 )

(3, 18)

(4, 20)

Step 2

Step 3

L o o k f o r a p a t t e r n i n t h e ta b le. D e s c r ib e t h e p a t t e r n i n w o r d s so y o u c a n w r it e

a n e q u a t io n t o r e p r e s e n t t h e r e la t io n s h ip.

Words Multiply the number of rectangles in each figure by 2 to get the

t o t a l le n g t h o f t h e t o p a n d b o t t o m s id e s o f t h e c o m b in e d fig u r e.

T h e n a d d 2 (6 ), o r 12, f o r t h e t o t a l le n g t h o f th e le f t a n d r i g h t s id e s

o f th e c o m b in e d f ig u r e t o g e t t h e e n t ir e p e r im e te r.

Equation y = 2x + 12

Use the table to make a graph.

W i t h a g ra p h , y o u c a n see a p a t t e r n

fo rm e d by the re la tio n sh ip betw een the

num ber of rectangles and the perim eter

of the combined figure.

24

16

8

0

Use th e y-axis fo r the

d e pend ent variable.

0 1 2 3 4

Use th e x-axis fo r the

Go t I t? 1. a. I n t h e d ia g r a m b e lo w , w h a t is th e independent variable.

re la tio n sh ip betw een the n u m b e r

o f t r ia n g le s a n d t h e p e r im e t e r o f t h e f ig u r e t h e y f o r m? R e p r e s e n t t h is

relationship using a table, w ords, an equation, and a graph.

4 4 4

2 tria n g le s 3 tria n g le s 4 tria n g le s

b. R e a so n in g S u p p o s e y o u k n o w th e p e r im e t e r o f n tria n g le s. W h a t w o u ld

you do to find the perim eter o f n + 1 triangles?

c. H o w d o e s y o u r a n s w e r to p a r t ( b ) r e la te to th e e q u a tio n y o u w r o te i n p a r t (a)?

You can describe the relationship in Problem 1 by saying

t h a t t h e p e r im e t e r is a f u n c t i o n o f th e n u m b e r o f re c ta n g le s.

A fu n ctio n is a r e la t io n s h ip t h a t p a ir s e a c h i n p u t v a lu e w i t h

exactly one output value.

Y o u h a v e s e e n t h a t o n e w a y t o r e p r e s e n t a f u n c t i o n is w i t h

a graph. A lin ea r fu n c tio n is a fu n c tio n w h o s e g ra p h is a

n o n v e r t ic a l l in e o r p a r t o f a n o n v e r t ic a l lin e.

Input

(independent

variable)

yzi_

Function (exactly

one output

per input)

Ly

r\

Output

(dependent

variable)

PowerAlgebra.com Lesson 4-2 Patterns and Linear Functions^241