Algebra 1 Common Core Student Edition, Grade 8-9

One relationship

is b e tw e e n th e

le n g th o f a shadow

and th e tim e o f

day.

MATHEMATICAL

PRACTICES

Patterns and

Linear Functions

@ Common Core State Standards

A-REI.D.10 Understand that the graph of an equation

in tw o variables is the set o f all its solutions plotted in

the coordinate plane, often fo rm in g a curve (which could

be a line). Also F-IF.B.4

M P 1, M P 2, MP 3, M P 4

Object ive T o i d e n t i f y a n d r e p r e s e n t p a t t e r n s t h a t d e s c r ib e l in e a r f u n c t io n s

Lesso n

Vocabulary

dependent

variable

in d e p e n d e n t

variable

in p u t

output

function

lin e a r fu n c tio n

I

In the Solve It, you identified variables whose value depends o n t h e v a lu e o f a n o t h e r v a r ia b le.

In a relationship betw een variables, the dependent variable changes in response to

another variable, the in d ep en d en t variable. Values of the independent variable are

called inputs. V a lu e s o f th e d e p e n d e n t v a r ia b le a re c a lle d outputs.

Esse n t i a l U n d e r st a n d i n g T h e v a lu e o f o n e v a r ia b le m a y b e u n i q u e ly

d e t e r m in e d b y th e v a lu e o f a n o t h e r v a r ia b le. S u c h r e la t io n s h ip s m a y b e r e p r e s e n te d

u s in g ta b le s , w o r d s , e q u a tio n s , se ts o f o r d e r e d p a ir s , a n d g ra p h s.

Rep r esen t i n g a Geo m et r i c Rel at i o n sh i p

In the diagram below, what is the relationship between the number of rectangles

and the perimeter of the figure they form? Represent this relationship using a

table, words, an equation, and a graph.

1 1 1 1 1 1111

1 rectang le 2 rectangles 3 rectangles 4 rectangles

240 Chapter 4 An Introduction to Functions